Nonlinear three-point boundary value problems

Nontrivial Solutions for Singular Nonlinear Three-Point Boundary Value Problems

The singular nonlinear three-point boundary value problems { −(Lu)(t) = h(t)f (u(t)), 0 < t < 1, βu(0)− γ u′(0) = 0, u(1) = αu(η) are discussed under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, where (Lu)(t) = (p(t)u′(t))′+q(t)u(t), 0 < η < 1, h(t) is allowed to be singular at both t = 0 and t = 1, and f need not be nonnegative. The associated ...

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Nonlinear Three Point Boundary Value Problem

In this work, we establish sufficient conditions for the existence of solutions for a three point boundary value problem generated by a third order differential equation. We give sufficient conditions that allow us to obtain the existence of a nontrivial solution. Then by using the Leray Schauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an a...

Sinc-Galerkin method for solving a class of nonlinear two-point boundary value problems

In this article, we develop the Sinc-Galerkin method based on double exponential transformation for solving a class of weakly singular nonlinear two-point boundary value problems with nonhomogeneous boundary conditions. Also several examples are solved to show the accuracy efficiency of the presented method. We compare the obtained numerical results with results of the other existing methods in...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation