Green’s function and existence of solutions for a third-order three-point boundary value problem

Mathematical Modelling and Analysis

卷:24

Sergey Smirnov¹ 

[1] Institute of Mathematics and Computer Science, University of Latvia, Raina bulvaris 29, Riga, LV-1459, Latvia;

关键词: Green’s function;    nonlinear boundary value problems;    three-point boundary conditions;    existence and uniqueness of solutions;   

DOI  :  10.3846/mma.2019.012

来源: DOAJ

【 摘 要 】

The solutions of third-order three-point boundary value problemx‘‘‘ + f(t, x) = 0, t ∈ [a, b], x(a) = x‘(a) = 0, x(b) = kx(η),where η ∈ (a, b), k ∈ R, f ∈ C([a, b] × R, R) and f(t, 0) ≠ 0, are the subject of this investigation. In order to establish existence and uniqueness results for the solutions, attention is focused on applications of the corresponding Green’s function. As an application, also one example is given to illustrate the result. Keywords: Green’s function, nonlinear boundary value problems, three-point boundary conditions, existence and uniqueness of solutions.

【 授权许可】

Unknown