Some existence results of positive solutions for p-Laplacian systems

Peng Wang,Yuanfang Ru

doi:10.1186/s13661-019-1124-1

Abstract

In this paper, we establish several new existence theorems for positive solutions of systems of (2n,2m)-order of two p-Laplacian equations. The results are based on the Krasnosel’skii fixed point theorem and mainly complement those of Djebali, Moussaoui, and Precup.

Highlights

1 Introduction Quasilinear elliptic systems have been used in a great variety of applications, and existence results and a priori estimates of positive solutions for quasilinear elliptic systems have been broadly investigated
In [2] the authors proved a priori estimates for the solutions of elliptic systems involving quasilinear operators in divergence form in an open set Ω ⊂ RN and, as a consequence, obtained theorems on nonexistence of positive solutions in the case Ω = RN
Equations of the p-Laplacian form occur in the study of non-Newtonian fluid theory and the turbulent flow of a gas in a porous medium

Summary

Introduction

Quasilinear elliptic systems have been used in a great variety of applications, and existence results and a priori estimates of positive solutions for quasilinear elliptic systems have been broadly investigated. The first existence result is obtained via the classical Krasnosel’skii fixed point theorem of cone compression and expansion under the following notation and assumptions. The second existence result is obtained via the vector versions of the Krasnosel’skii fixed point theorem [13] under the following notation and assumptions.

Results

Conclusion