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

• Published in: Mathematical modelling and analysis Vol. 24; no. 2; pp. 171 - 178
• Main Author: Smirnov, Sergey
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 05.02.2019
• Subjects: Boundary conditions; Boundary value problems; existence and uniqueness of solutions; Green’s function; nonlinear boundary value problems; three-point boundary conditions; Uniqueness; existence and uniqueness of solutions; Green’s function; nonlinear boundary value problems; three-point boundary conditions
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2019.012

The solutions of third-order three-point boundary value problem x‘‘‘ + 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.