Resonant p-Laplacian problems with functional boundary conditions

Weihua Jiang,Nickolai Kosmatov

doi:10.1186/s13661-018-0986-y

Abstract

By constructing a suitable projection scheme and using the extension of Mawhin’s continuation theorem, the existence of solution for functional p-Laplacian boundary value problems at resonance is studied. The paper is a generalization of some current results to a fully nonlinear case.

Highlights

1 Introduction A boundary value problem is said to be at resonance if the corresponding homogeneous boundary value problem has a non-trivial solution
In Refs. [6, 9], the authors studied the existence of solutions for functional boundary value problems with a linear differential operator by using Mawhin’s continuation theorem
Since the p-Laplacian operator occurs in many applications such as non-Newtonian mechanics, nonlinear elasticity and glaciology, combustion theory, we would like to further extend the results of [6] to the third-order functional p-Laplacian boundary value problem at resonance

Summary

Introduction

A boundary value problem is said to be at resonance if the corresponding homogeneous boundary value problem has a non-trivial solution. [6, 9], the authors studied the existence of solutions for functional boundary value problems with a linear differential operator by using Mawhin’s continuation theorem.

Results

Conclusion