Third order differential equations with integral boundary conditions (original) (raw)
Related papers
Existence and uniqueness of solutions for the system of first-order nonlinear differential equations with three-point and integral boundary conditions, 2019
In the paper, the existence and uniqueness of the solutions for the system of the non-linear first-order ordinary differential equations with three-point and integral boundary conditions are studied. The Green function is constructed and the considered problem is reduced to the equivalent integral equation. The existence and uniqueness of the solutions for the given problem are analyzed by using the Banach contraction principle. The Schaefer's fixed point theorem is then used to prove the existence of the solutions. Finally, the examples are given to verify the given theorems.
Existence of solutions of third-order functional problems with nonlinear boundary conditions
The ANZIAM Journal, 2004
In this paper some existence results for third-order differential equations with nonlinear boundary value conditions are derived. Functional dependence in the data is allowed. In the proofs we use the method of upper and lower solutions, Schauder's fixed point theorem and results from Cabada and Heikkilä on third-order differential equations with linear and nonfunctional initial-boundary value conditions.
Solvability for a nonlinear third-order three-point boundary value problem
Universal journal of mathematics and applications, 2018
In this article, the existence of positive solutions for a nonlinear third-order three-point boundary value problem with integral condition is investigated. By using Leray-Schauder fixed point theorem, sufficient conditions for the existence of at least one positive solution are obtained. Illustrative examples are also presented to show the applicability of our results.
Filomat
In this paper the existence and uniqueness of the solutions to boundary value problems for the first order non-linear system of the ordinary differential equations with three-point boundary conditions are investigated. For the first time the Green function is constructed and the considered problem is reduced to the equivalent integral equations that allow us to prove the existence and uniqueness theorems in differ from existing works, applying the Banach contraction mapping principle and Schaefer?s fixed point theorem. An example is given to illustrate the obtained results.
A third order boundary value problem subject to nonlinear boundary conditions
2010
Abstract. Utilizing the theory of fixed point index for compact maps, we establish new results on the existence of positive solutions for a certain third order boundary value problem. The boundary conditions that we study are of nonlocal type, involve Stieltjes integrals and are allowed to be nonlinear.
Existence Solutions for Three Point Boundary Value Problem for Differential Equations
In this paper, under weak assumptions, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer and krasnoselskii’s fixed point theorem. At the end, some illustrative examples are presented.
On some third order nonlinear boundary value problems
Journal of Mathematical Analysis and Applications, 2008
We prove an Ambrosetti-Prodi type result for the third order fully nonlinear equationu'''(t)+f(t,u(t),u'(t),u''(t))=sp(t) with and continuous functions, , under several two-point separated boundary conditions. From a Nagumo-type growth condition, an a priori estimate on u'' is obtained. An existence and location result will be proved, by degree theory, for such that there exist lower and upper solutions. The location part can be used to prove the existence of positive solutions if a non-negative lower solution is considered. The existence, nonexistence and multiplicity of solutions will be discussed as s varies.