Multiple positive solutions for a second-order boundary value problem with integral boundary conditions

Multiple positive solutions for a second-order boundary value problem with integral boundary conditions

where α and β are nonnegative constants. Boundary value problems of ordinary differential equations arise in kinds of different areas of applied mathematics and physics. Many authors have studied two-point, threepoint, multi-point boundary value problems for second-order differential equations extensively, see [–] and the references therein. In recent years, boundary value problems with integ...

Existence of Positive Solutions of a Nonlinear Second-order Boundary-value Problem with Integral Boundary Conditions

In this article we prove the existence of at least one positive solution for a three-point integral boundary-value problem for a second-order nonlinear differential equation. The existence result is obtained by using Schauder’s fixed point theorem. Therefore, we do not need local assumptions such as superlinearity or sublinearity of the involved nonlinear functions.

Second-Order Boundary Value Problem with Integral Boundary Conditions

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...

Positive Solutions for Second-order Boundary Value Problem with Integral Boundary Conditions at Resonance on a Half-line

This paper deals with the second order boundary value problem with integral boundary conditions on a half-line: (p(t)x′(t))′ + g(t)f(t, x(t)) = 0, a.e. in (0,∞), x(0) = ∫ ∞ 0 x(s)g(s)ds, lim t→∞ p(t)x′(t) = p(0)x′(0). A new result on the existence of positive solutions is obtained. The interesting points are: firstly, the boundary value problem involved in the integral boundary condition on unb...