Positive solutions for a p−q‐Laplacian system with critical nonlinearities

Abstract

In this paper, our main purpose is to establish the existence results of positive solutions for a p − q-Laplacian system involving concave-convex nonlinearities:where Ω is a bounded domain in R N , , > 0 and 1 < r < q < p < N. We assume 1 < , and + = p * = Np N−p is the critical Sobolev exponent and △ s · = div(|∇ · | s−2 ∇·) is the s-Laplacian operator. The main results are obtained by variational methods.

A multiplicity results to a p-q Laplacian system with a concave and singular nonlinearities

“…where a+b = p * . Ding and Xiao [11] studied (1.3) with the p−superlinear perturbation of 2 ≤ p ≤ r < p * an extension of which can be found in Yin [33]. Both the works in [33] and [11] have obtained the existence of cat(Ω) number of solutions using the Lusternik-Scnirelman category.…”

“…Ding and Xiao [11] studied (1.3) with the p−superlinear perturbation of 2 ≤ p ≤ r < p * an extension of which can be found in Yin [33]. Both the works in [33] and [11] have obtained the existence of cat(Ω) number of solutions using the Lusternik-Scnirelman category. Similar results for elliptic equations driven by the p-Laplacian or the double phase operator can be found in [22,24].…”