Existence and multiplicity of nontrivial solutions for‎ ‎$p$-Laplacian system with nonlinearities of concave-convex type and‎ ‎sign-changing weight functions

Khademloo, S.; Khanjany Ghazi, S.

Existence and multiplicity of nontrivial solutions for‎ ‎$p$-Laplacian system with nonlinearities of concave-convex type and‎ ‎sign-changing weight functions

Document Type : Research Paper

Authors

S. Khademloo ¹

S. Khanjany Ghazi ²

¹ Department of basic sciences, babol noushirvani university of technology, babol, Iran

² Babol university of technology

Abstract

This paper is concerned with the existence of multiple positive‎
‎solutions for a quasilinear elliptic system involving concave-convex‎
‎nonlinearities‎
‎and sign-changing weight functions‎. ‎With the help of the Nehari manifold and Palais-Smale condition‎,
‎we prove that the system has at least two nontrivial positive‎
‎solutions‎, ‎when the pair of parameters $(\lambda,\mu)$ belongs to a certain subset of $\mathbb{R}^2$‎.

Keywords

variational methods‎

‎Nehari manifold‎

‎Dirichlet boundary condition‎

‎sign-changing weight functions‎

Subjects