Radu Precup - Profile on Academia.edu (original) (raw)

Papers by Radu Precup

Topological Methods in Nonlinear Analysis, Apr 23, 2012

Fixed point theorems of Krasnosel'skiȋ type are obtained for the localization of positive solutio... more Fixed point theorems of Krasnosel'skiȋ type are obtained for the localization of positive solutions in a set defined by means of the norm and of a semi-norm. In applications to elliptic boundary value problems, the semi-norm comes from the Moser-Harnack inequality for nonnegative superharmonic functions whose use is crucial for the estimations from below. The paper complements and gives a fixed point alternative approach to our similar results recently established in the frame of critical point theory. It also provides a new method for discussing the existence and multiplicity of positive solutions to elliptic boundary value problems.

Topological Methods in Nonlinear Analysis, Jun 1, 1995

Topological Methods in Nonlinear Analysis, May 22, 2017

Two critical point theorems of M. Schechter in a ball of a Hilbert space are extended to uniforml... more Two critical point theorems of M. Schechter in a ball of a Hilbert space are extended to uniformly convex Banach spaces by exploiting the properties of the duality mapping. Moreover, the critical points are sought in the intersection of a ball with a wedge, in particular with a cone, making possible applications to positive solutions of variational problems. The extension from Hilbert to Banach spaces not only requires a major refining of reasoning, but also a different statement by adding a third possibility to the original two alternatives from Schechter's results. The theory is applied to positive solutions for p-Laplace equations.

We study the existence of nontrivial solutions to the boundaryvalue problem and to the system whe... more We study the existence of nontrivial solutions to the boundaryvalue problem and to the system where c, c 1 , c 2 , λ, λ 1 , λ 2 are real positive constants and the nonlinearities f and g satisfy suitable conditions. The proofs are based on fixed point theorems. 2000 Mathematics Subject Classification. 34B40.

In this paper, we extend the existence results presented in for L p spaces to operator inclusions... more In this paper, we extend the existence results presented in for L p spaces to operator inclusions of Hammerstein type in W 1,p spaces. We also show an application of our results to anti-periodic boundary-value problems of second-order differential equations with nonlinearities depending on u .

Studia Universitatis Babeş-Bolyai, Mar 8, 2020

The paper deals with systems of abstract integrodifferential equations subject to general nonloca... more The paper deals with systems of abstract integrodifferential equations subject to general nonlocal initial conditions. In order to allow the nonlinear terms of the equations to behave independently as much as possible, we use a vector approach based on matrices, vector-valued norms and a vector version of Krasnoselskii's fixed point theorem for a sum of two operators. The assumptions take into account the support of the nonlocal initial conditions and the hybrid character of the system. Two examples are given to illustrate the theory.

Carpathian Journal of Mathematics

The starting point is an approximation process consisting of linear and positive operators. The p... more The starting point is an approximation process consisting of linear and positive operators. The purpose of this note is to establish the limit of the iterates of some multidimensional approximation operators. The main tool is a Perov's result which represents a generalization of Banach fixed point theorem. In order to support the theoretical aspects, we present three applications targeting respectively the operators Bernstein, Cheney-Sharma and those of binomial type. The last class involves an incursion into umbral calculus.

Abstract. We study the existence of nontrivial solutions to the boundary-value problem −u′ ′ + cu... more Abstract. We study the existence of nontrivial solutions to the boundary-value problem −u′ ′ + cu ′ + λu = f(x, u), − ∞ < x < +∞, u(−∞) = u(+∞) = 0 and to the system −u′ ′ + c1u ′ + λ1u = f(x, u, v), − ∞ < x < +∞, −v′ ′ + c2v ′ + λ2v = g(x, u, v), − ∞ < x < +∞,

Journal of Applied Analysis & Computation, 2018

arXiv: Classical Analysis and ODEs, 2015

We study the existence and multiplicity of positive solutions for a nonlinear fourth-order two-po... more We study the existence and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnoselskii's compression-expansion theorem, and unilateral Harnack type inequalities.

Topological Methods in Nonlinear Analysis, 2007

In this paper the compression-expansion fixed point theorems are extended to operators which are ... more In this paper the compression-expansion fixed point theorems are extended to operators which are compositions of two multi-valued nonlinear maps and satisfy compactness conditions of Monch type with respect to the weak or the strong topology. As an application, the existence of positive solutions for ppp-Laplace inclusions is studied.

Mediterranean Journal of Mathematics, 2021

A direct variational technique involving Clarke generalized gradient is used to treat general bou... more A direct variational technique involving Clarke generalized gradient is used to treat general boundary value problems with discontinuous nonlinearities. Based on the theory of positive definite symmetric operators it is established the nonsmooth variational form of the regularized inclusions which give the Filippov solutions of the discontinuous problems. These solutions reduce to classical solutions in case that a transversality condition on the set of discontinuities is satisfied. The results apply to a wide class of concrete boundary value problems of different orders. Two illustrative examples are given.

Studia Universitatis Babes-Bolyai Matematica, 2020

Topological Methods in Nonlinear Analysis, 1995

Journal of Mathematical Analysis and Applications, 2011

We obtain existence and localization results of positive nontrivial solutions for a class of semi... more We obtain existence and localization results of positive nontrivial solutions for a class of semilinear elliptic variational systems. The proof is based on variants of Schechter's localized critical point theorems for Hilbert spaces not identified to their duals and on the technique of inverse-positive matrices. The Leray-Schauder boundary condition is also involved.

Journal of Mathematical Analysis and Applications, 2015

The main purpose of this paper is to make Krasnoselskii's compression-expansion fixed point t... more The main purpose of this paper is to make Krasnoselskii's compression-expansion fixed point theorem applicable to nonlinear integral equations in ordered Banach spaces.

This survey paper presents the new method worked out in [14] and [15] for the existence and local... more This survey paper presents the new method worked out in [14] and [15] for the existence and localization of solutions to evolution operator equations, which is based on Krasnoselskii's compression-expansion fixed point theorem in cones. The main idea is to handle two equivalent operator forms of the equation, one of fixed point type giving the operator to which Krasnoselskii's theorem applies and an other one of coincidence type which is used to localize a positive solution in a shell. Applications are presented for a boundary value problem associated to a fourth order partial differential equation on a rectangular domain and for nonlinear wave equations.

An integral inequality is deduced from the negation of the geometrical condition in the bounded m... more An integral inequality is deduced from the negation of the geometrical condition in the bounded mountain pass theorem of Schechter, in a situation where this theorem does not apply. Also two localization results of non-zero solutions to a superlinear boundary value problem are established.

Mathematica Slovaca, 2014

In this paper we present Perov type fixed point theorems for contractive mappings in Gheorghiu’s ... more In this paper we present Perov type fixed point theorems for contractive mappings in Gheorghiu’s sense on spaces endowed with a family of vector-valued pseudo-metrics. Applications to systems of integral equations are given to illustrate the theory. The examples also prove the advantage of using vector-alued pseudo-metrics and matrices that are convergent to zero, for the study of systems of equations.

Topological Methods in Nonlinear Analysis, Apr 23, 2012

Fixed point theorems of Krasnosel'skiȋ type are obtained for the localization of positive solutio... more Fixed point theorems of Krasnosel'skiȋ type are obtained for the localization of positive solutions in a set defined by means of the norm and of a semi-norm. In applications to elliptic boundary value problems, the semi-norm comes from the Moser-Harnack inequality for nonnegative superharmonic functions whose use is crucial for the estimations from below. The paper complements and gives a fixed point alternative approach to our similar results recently established in the frame of critical point theory. It also provides a new method for discussing the existence and multiplicity of positive solutions to elliptic boundary value problems.

Topological Methods in Nonlinear Analysis, Jun 1, 1995

Topological Methods in Nonlinear Analysis, May 22, 2017

Two critical point theorems of M. Schechter in a ball of a Hilbert space are extended to uniforml... more Two critical point theorems of M. Schechter in a ball of a Hilbert space are extended to uniformly convex Banach spaces by exploiting the properties of the duality mapping. Moreover, the critical points are sought in the intersection of a ball with a wedge, in particular with a cone, making possible applications to positive solutions of variational problems. The extension from Hilbert to Banach spaces not only requires a major refining of reasoning, but also a different statement by adding a third possibility to the original two alternatives from Schechter's results. The theory is applied to positive solutions for p-Laplace equations.

We study the existence of nontrivial solutions to the boundaryvalue problem and to the system whe... more We study the existence of nontrivial solutions to the boundaryvalue problem and to the system where c, c 1 , c 2 , λ, λ 1 , λ 2 are real positive constants and the nonlinearities f and g satisfy suitable conditions. The proofs are based on fixed point theorems. 2000 Mathematics Subject Classification. 34B40.

In this paper, we extend the existence results presented in for L p spaces to operator inclusions... more In this paper, we extend the existence results presented in for L p spaces to operator inclusions of Hammerstein type in W 1,p spaces. We also show an application of our results to anti-periodic boundary-value problems of second-order differential equations with nonlinearities depending on u .

Studia Universitatis Babeş-Bolyai, Mar 8, 2020

The paper deals with systems of abstract integrodifferential equations subject to general nonloca... more The paper deals with systems of abstract integrodifferential equations subject to general nonlocal initial conditions. In order to allow the nonlinear terms of the equations to behave independently as much as possible, we use a vector approach based on matrices, vector-valued norms and a vector version of Krasnoselskii's fixed point theorem for a sum of two operators. The assumptions take into account the support of the nonlocal initial conditions and the hybrid character of the system. Two examples are given to illustrate the theory.

Carpathian Journal of Mathematics

The starting point is an approximation process consisting of linear and positive operators. The p... more The starting point is an approximation process consisting of linear and positive operators. The purpose of this note is to establish the limit of the iterates of some multidimensional approximation operators. The main tool is a Perov's result which represents a generalization of Banach fixed point theorem. In order to support the theoretical aspects, we present three applications targeting respectively the operators Bernstein, Cheney-Sharma and those of binomial type. The last class involves an incursion into umbral calculus.

Abstract. We study the existence of nontrivial solutions to the boundary-value problem −u′ ′ + cu... more Abstract. We study the existence of nontrivial solutions to the boundary-value problem −u′ ′ + cu ′ + λu = f(x, u), − ∞ < x < +∞, u(−∞) = u(+∞) = 0 and to the system −u′ ′ + c1u ′ + λ1u = f(x, u, v), − ∞ < x < +∞, −v′ ′ + c2v ′ + λ2v = g(x, u, v), − ∞ < x < +∞,

Journal of Applied Analysis & Computation, 2018

arXiv: Classical Analysis and ODEs, 2015

We study the existence and multiplicity of positive solutions for a nonlinear fourth-order two-po... more We study the existence and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnoselskii's compression-expansion theorem, and unilateral Harnack type inequalities.

Topological Methods in Nonlinear Analysis, 2007

In this paper the compression-expansion fixed point theorems are extended to operators which are ... more In this paper the compression-expansion fixed point theorems are extended to operators which are compositions of two multi-valued nonlinear maps and satisfy compactness conditions of Monch type with respect to the weak or the strong topology. As an application, the existence of positive solutions for ppp-Laplace inclusions is studied.

Mediterranean Journal of Mathematics, 2021

A direct variational technique involving Clarke generalized gradient is used to treat general bou... more A direct variational technique involving Clarke generalized gradient is used to treat general boundary value problems with discontinuous nonlinearities. Based on the theory of positive definite symmetric operators it is established the nonsmooth variational form of the regularized inclusions which give the Filippov solutions of the discontinuous problems. These solutions reduce to classical solutions in case that a transversality condition on the set of discontinuities is satisfied. The results apply to a wide class of concrete boundary value problems of different orders. Two illustrative examples are given.

Studia Universitatis Babes-Bolyai Matematica, 2020

Topological Methods in Nonlinear Analysis, 1995

Journal of Mathematical Analysis and Applications, 2011

We obtain existence and localization results of positive nontrivial solutions for a class of semi... more We obtain existence and localization results of positive nontrivial solutions for a class of semilinear elliptic variational systems. The proof is based on variants of Schechter's localized critical point theorems for Hilbert spaces not identified to their duals and on the technique of inverse-positive matrices. The Leray-Schauder boundary condition is also involved.

Journal of Mathematical Analysis and Applications, 2015

The main purpose of this paper is to make Krasnoselskii's compression-expansion fixed point t... more The main purpose of this paper is to make Krasnoselskii's compression-expansion fixed point theorem applicable to nonlinear integral equations in ordered Banach spaces.

This survey paper presents the new method worked out in [14] and [15] for the existence and local... more This survey paper presents the new method worked out in [14] and [15] for the existence and localization of solutions to evolution operator equations, which is based on Krasnoselskii's compression-expansion fixed point theorem in cones. The main idea is to handle two equivalent operator forms of the equation, one of fixed point type giving the operator to which Krasnoselskii's theorem applies and an other one of coincidence type which is used to localize a positive solution in a shell. Applications are presented for a boundary value problem associated to a fourth order partial differential equation on a rectangular domain and for nonlinear wave equations.

An integral inequality is deduced from the negation of the geometrical condition in the bounded m... more An integral inequality is deduced from the negation of the geometrical condition in the bounded mountain pass theorem of Schechter, in a situation where this theorem does not apply. Also two localization results of non-zero solutions to a superlinear boundary value problem are established.

Mathematica Slovaca, 2014

In this paper we present Perov type fixed point theorems for contractive mappings in Gheorghiu’s ... more In this paper we present Perov type fixed point theorems for contractive mappings in Gheorghiu’s sense on spaces endowed with a family of vector-valued pseudo-metrics. Applications to systems of integral equations are given to illustrate the theory. The examples also prove the advantage of using vector-alued pseudo-metrics and matrices that are convergent to zero, for the study of systems of equations.