Green's Function and Existence of a Unique Solution for a Third-Order Three-Point Boundary Value Problem - Smirnov, Sergey (Mathematical modelling and analysis, 2019)
The solutions of third-order three-point boundary value problem x"' + f (t,x) = 0, t [member of] [a,b], x(a) = x'(a) = 0, x(b) = kx([eta]), where [eta] [member of] (a,b), k [member of] R, f [member of] C([a,b] x R, R) and f (t, 0) [not equal to] 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. AMS Subject Classification: 34B10; 34B15.