Existence of Multiple Positive Solutions for Quasilinear Elliptic Systems Involving Critical Hardy–Sobolev Exponents and Sign-Changing Weight Function

Abstract

In this paper, we consider a class of quasilinear elliptic systems with weights and the nonlinearity involving the critical Hardy–Sobolev exponent and one sign-changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.

Keywords:

• multiple positive solutions
• Nehari manifold
• critical Hardy–Sobolev exponent

AMS Subject Classification:

• 35A15
• 35B33
• 35J70