In this paper, we present the Green’s functions for a second-order linear differential equation with three-point boundary conditions. We give exact expressions of the solutions for the linear three-point boundary problems by the Green’s functions. As applications, we study uniqueness and iteration of the solutions for a nonlinear singular second-order three-point boundary value problem.

‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...

this paper studies a fractional boundary value problem of nonlineardifferential equations of arbitrary orders. new existence and uniquenessresults are established using banach contraction principle. other existenceresults are obtained using schaefer and krasnoselskii fixed point theorems.in order to clarify our results, some illustrative examples are alsopresented.

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....

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

a class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional bratu's problem are presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. associated bound...

In this paper, by Leggett-William fixed point theorem, we establish the existence of triple positive solutions of a new kind of integral boundary value problem for the nonlinear singular differential equations with p-Laplacian operator, in which q(t) can be singular at t = 0, 1. We also show that the results obtained can be applied to study certain higher order mixed boundary value problems. At...

We establish comparison and existence theorems of viscosity solutions of the initial-boundary value problem for some singular degenerate parabolic partial di/erential equations with nonlinear oblique derivative boundary conditions. The theorems cover the capillary problem for the mean curvature 1ow equation and apply to more general Neumann-type boundary problems for parabolic equations in the ...

The limiting behavior of the unique solution to Maxwell's equations in an exterior domain with a Leontovich boundary condition as the impedance tends to zero is investigated. This is accomplished by reducing the impedance boundary value problem for the Maxwell equations to a system of three integral equations. It is shown that the Leontovich boundary condition leads to a singular perturbation p...