On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation

On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation

This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the ...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

On the Boundary Integral Equation Method for a Mixed Boundary Value Problem of the Biharmonic Equation

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation

and Applied Analysis 3 For existence theorems for fractional differential equations and applications, we refer to the survey 14 . Concerning the definitions and basic properties, we refer the reader to 15 . 2. Preliminaries and Previous Results For the convenience of the reader, we present here some definitions, lemmas, and results that will be used in the proofs of our main results. Definition...