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

Papers by Radu Precup

Electronic Journal of Qualitative Theory of Differential Equations

The paper deals with the existence and localization of positive radial solutions for stationary p... more The paper deals with the existence and localization of positive radial solutions for stationary partial differential equations involving a general ϕ -Laplace operator in the annulus. Three sets of boundary conditions are considered: Dirichlet–Neumann, Neumann–Dirichlet and Dirichlet–Dirichlet. The results are based on the homotopy version of Krasnosel'skii's fixed point theorem and Harnack type inequalities, first established for each one of the boundary conditions. As a consequence, the problem of multiple solutions is solved in a natural way. Numerical experiments confirming the theory, one for each of the three sets of boundary conditions, are performed by using the MATLAB object-oriented package Chebfun.

Mathematics, 2019

We establish the existence of positive solutions for systems of second–order differential equatio... more We establish the existence of positive solutions for systems of second–order differential equations with discontinuous nonlinear terms. To this aim, we give a multivalued vector version of Krasnosel’skiĭ’s fixed point theorem in cones which we apply to a regularization of the discontinuous integral operator associated to the differential system. We include several examples to illustrate our theory.

Advances in Nonlinear Analysis, 2019

We propose a method for the localization of solutions for a class of nonlinear problems arising i... more We propose a method for the localization of solutions for a class of nonlinear problems arising in the homogenization theory. The method combines concepts and results from the linear theory of PDEs, linear periodic homogenization theory, and nonlinear functional analysis. Particularly, we use the Moser-Harnack inequality, arguments of fixed point theory and Ekeland's variational principle. A significant gain in the homogenization theory of nonlinear problems is that our method makes possible the emergence of finitely or infinitely many solutions.

Nonlinear Analysis: Modelling and Control, 2019

This paper concerns the existence, localization and multiplicity of positive solutions for a φ-La... more This paper concerns the existence, localization and multiplicity of positive solutions for a φ-Laplacian problem with a perturbed term that may have discontinuities in the state variable. First, the initial discontinuous differential equation is replaced by a differential inclusion with an upper semicontinuous term. Next, the existence and localization of a positive solution of the inclusion is obtained via a compression-expansion fixed point theorem for a composition of two multivalued maps, and finally, a suitable control of discontinuities allows to prove that any solution of the inclusion is a solution in the sense of Carathéodory of the initial discontinuous equation. No monotonicity assumptions on the nonlinearity are required.

Applicable Analysis, 2015

The paper presents a vectorial approach for coupled general nonlinear Schrödinger systems with no... more The paper presents a vectorial approach for coupled general nonlinear Schrödinger systems with nonlocal Cauchy conditions. Based on fixed point principles, the use of matrices with spectral radius less than one, and on basic properties of the Schrödinger solution operator, several existence results are obtained. The essential role of the support of the nonlocal Cauchy condition is emphasized and fully exploited.

Journal of Mathematical Analysis and Applications, 2008

In this paper we present a compression type version of the mountain pass lemma in a conical shell... more In this paper we present a compression type version of the mountain pass lemma in a conical shell with respect to two norms. An application to second-order ordinary differential equations is included.

Dynamics of Partial Differential Equations, 2015

In this paper we develop a new theory for the existence, localization and multiplicity of positiv... more In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational, quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework for the existence of fixed points of nonlinear operators acting on cones that satisfy an inequality of Harnack type. Our methodology relies on fixed point index theory. We also provide a non-existence result and an example to illustrate the theory.

Applied Mathematics Letters, 2011

By using the bilinear form and the Leray-Schauder principle, we prove the new antiperiodic existe... more By using the bilinear form and the Leray-Schauder principle, we prove the new antiperiodic existence results for second order differential equations.

Zeitschrift für Analysis und ihre Anwendungen, 2003

Existence and localization results for the nonlinear wave equation are established by Krasnoselsk... more Existence and localization results for the nonlinear wave equation are established by Krasnoselskii's compression-expansion fixed point theorem in cones. The main idea is to handle two equivalent operator forms of the wave equation, one of fixed point type giving the operator to which Krasnoselskii's theorem applies and an other one of coincidence type for the localization of a solution. In this way, the compression-expansion technique is extended from scalar equations to abstract equations, specifically to partial dierential equations.

Journal of Mathematical Analysis and Applications, 2009

Existence, localization and multiplicity results of positive solutions to a system of singular se... more Existence, localization and multiplicity results of positive solutions to a system of singular second-order differential equations are established by means of the vector version of Krasnoselskii's cone fixed point theorem. The results are then applied for positive radial solutions to semilinear elliptic systems.

Journal of Mathematical …, 2012

In this paper we continue the investigation of a basic mathematical model describing the dynamics... more In this paper we continue the investigation of a basic mathematical model describing the dynamics of three cell lines after allogeneic stem cell transplantation: normal host cells, leukemic host cells and donor cells, whose evolution ultimately lead either to the normal hematopoietic state achieved by the expansion of the donor cells and the elimination of the host cells, or to the leukemic hematopoietic state characterized by the proliferation of the cancer line and the suppression of the other cell lines. A theoretical basis for the control of post-transplant evolution is provided. We describe several scenarios of change of system parameters by which a bad posttransplant evolution can be corrected and turned into a good one and we propose therapy planning algorithms for guiding the correction treatment.

Boundary Value Problems, 2009

In the last few decades, fractional-order models are found to be more adequate than integer-order... more In the last few decades, fractional-order models are found to be more adequate than integer-order models for some real world problems. Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and ...

Journal of Fixed Point Theory and Applications, 2007

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