Infinitely many solutions for semilinear elliptic problems with sign-changing weight functions

Abstract

In this paper, we study the elliptic problem

where is the critical Sobolev exponent, and or is a sign-changing function. Under different assumptions on and we prove the existence of infinitely many solutions to the above problem. We also show that one of these solutions is positive.

Keywords:

• elliptic problem
• sign-changing weight function
• infinitely many solutions
• positive solution
• Nehari manifold

AMS Subject Classifications:

• 35J91
• 35J20
• 47J30

Acknowledgments

Andrzej Szulkin is supported in part by the Swedish Research Council.