Multiple positive solutions for equations involving critical Sobolev exponent in R^N

Abstract

$$ -{ m div }(|abla u|^{m-2}abla u) = lambda h u^q+u^{m^*-1},quad{ m in}quad R^N,. $$ Using the Ekeland Variational Principle and the Mountain Pass Theorem, we show the existence of $lambda ^*>0$ such that there are at least two non-negative solutions for each $lambda$ in $(0,lambda ^*)$.

Keywords

• Mountain Pass Theorem
• Ekeland Variational Principle.