Existence and iteration of positive solution for fractional integral boundary value problems with p-Laplacian operator

Ying He,Bo Bi

doi:10.1186/s13662-019-2317-8

Abstract

This paper is concerned with an integral boundary value problem of fractional differential equations with p-Laplacian operator. Sufficient conditions ensuring the existence of extremal solutions for the given problem are obtained. Our results are based on the method of upper and lower solutions and monotone iterative technique.

Highlights

1 Introduction This paper studies the existence of extremal solutions for the boundary value problem of a fractional p-Laplacian equation with the following form:
Being directly inspired by Wang [15], the purpose of this paper is to study the nonlinear integral boundary value problem for p-Laplacian differential equations
Applying the numerical scheme to Example 4.1, we obtain approximate solutions to un and vn for 1 ≤ n ≤ N , with N some integer

Summary

Introduction

This paper studies the existence of extremal solutions for the boundary value problem of a fractional p-Laplacian equation with the following form:. The monotone iterative technique, combined with the method of upper and lower solutions, provides an effective mechanism to prove constructive existence results for nonlinear differential equations, the advantage and importance of the technique needs no special emphasis [10, 11]. By using the monotone iterative technique, Ahmad He and Bi Advances in Difference Equations [12] and Alsaedi [13] successfully investigated initial value problems for nonlinear fractional differential equations with fractional derivatives. Being directly inspired by Wang [15], the purpose of this paper is to study the nonlinear integral boundary value problem for p-Laplacian differential equations. We construct two well-defined monotone iterative sequences of upper and lower solutions and prove that they converge uniformly to the actual solution of the problem

Preliminaries

15 Π then