关键词: 变号权函数, 多重性, Nehari流形

Abstract: We considered the multiplicity of weak solutions for a class of p-Laplacian elliptic equations with signchanging weight function. By means of Nehari’s manifold and logarithmic Sobolev inequality, we proved  that there were  at least two nontrivial weak solutions to the problem.

Key words: signchanging weight function, multiplicity, Nehari’s manifold