A fixed point operator for systems of vector p-Laplacian with singular weights

Xianghui Xu,Yong-Hoon Lee,Inbo Sim

doi:10.1186/s13661-016-0582-y

Xianghui Xu, Yong-Hoon Lee + Show 1 more

Open Access

https://doi.org/10.1186/s13661-016-0582-y

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Abstract

In this paper, after establishing a fixed point operator for a strongly coupled vector p-Laplacian with a singular and sign-changing weight function, which may not be integrable, we investigate the existence for the Dirichlet boundary value problems of strongly coupled vector p-Laplacian systems with a nonlinear term consisting of Hadamard product. The proofs are mainly based on topological degree arguments and the global continuation theorem.

Highlights

We are concerned with the existence of nontrivial solutions for strongly coupled nonlinear differential systems of the form
The goal of this paper is to get an existence result for (Pλ) where the differential operator is related to strongly coupled vector p-Laplacian and the weight function has stronger singularity at the boundary than L and sign-changing
In Section, we show the existence of solutions and give some illustrative examples, which satisfy all assumptions in the paper and are not given in other studies

Summary

Introduction

Since our problem involves systems of strongly coupled differential operators and the weight function h may change sign, related studies are not known yet, as far as the authors know. For a scalar equation of (Pλ), Sim and Lee [ ] established a new solution operator and proved an existence result by the global continuation theorem. The goal of this paper is to get an existence result for (Pλ) where the differential operator is related to strongly coupled vector p-Laplacian and the weight function has stronger singularity at the boundary than L and sign-changing.

Objectives

Results

Conclusion