Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions

Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions

It is well known that fourth-order boundary value problems (BVPs) arise in a variety of different areas of the flexibility mechanics and engineering physics and thus have been extensively studied; for instance, see [1–29] and references therein. Boundary value problems with integral boundary conditions appear in heat conduction, thermoelasticity, chemical engineering underground water flow, and...

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...

Higher order multi-point fractional boundary value problems with integral boundary conditions

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

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.