Fourth-order Three-point Boundary Value Research Articles

Existence of solutions for fourth order three-point boundary value problems on a half-line

In this paper, we apply Schauder's fixed point theorem, the upper and lower solution method, and topological degree theory to establish the existence of unbounded solutions for the following fourth order three-point boundary value problem on a half- line x 0000 (t) + q(t) f(t, x(t), x 0 (t), x 00 (t), x 000 (t)) = 0, t2 (0,+¥), x 00 (0) = A, x(h) = B1, x 0 (h) = B2, x 000 (+¥) = C, where h2 (0,+¥), but fixed, and f : (0,+¥) R 4 ! R satisfies Nagumo's condition. We present easily verifiable sufficient conditions for the existence of at least one solu- tion, and at least three solutions of this problem. We also give two examples to illustrate the importance of our results.

Solution of fourth order three-point boundary value problem using ADM and RKM

In this paper, a computational method is proposed, for solving linear and nonlinear fourth order three-point boundary value problem (BVP) and the system of nonlinear BVP. This method is based on the Adomian decomposition method (ADM) and the reproducing kernel method (RKM). The solution of linear fourth order three-point boundary value problem (BVP) is determined by the reproducing kernel method, and the solution of nonlinear fourth order three-point BVP is determined using the combination of Adomian decomposition method and reproducing kernel method. The approximate solutions are given in the form of series. Numerical results are shown to illustrate the accuracy of the present method.