Boundary Value Problem for Second-Order Differential Operators with Nonregular Integral Boundary Conditions

Second-Order Boundary Value Problem with Integral Boundary Conditions

Boundary Value Problem for Second-order Differential Operators with Mixed Nonlocal Boundary Conditions

In this paper, we study a second order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called non regular boundary conditions, we prove that the resolvent decreases with respect to the spec...

Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

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.