Existence and multiplicity of solutions for a class of p & q elliptic problems with critical exponent

Abstract

AbstractThis paper is concerned with the existence and multiplicity of nontrivial solutions to the following class of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$p \& q$\end{document} elliptic problems with critical exponent where \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\Omega \subset \mathbb {R}^{N}$\end{document} is a bounded smooth domain, N ≥ 3, λ is a positive parameter and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$a:\mathbb {R}\rightarrow \mathbb {R}$\end{document} is a function of C1 class. Here 1 < γ < N, γ < s < γ* or 1 < s < γ, where γ will be stated later.