Multiplicity and concentration results for a (p, q)-Laplacian problem in RN

In this paper, we study the multiplicity and concentration of positive solutions for the following (p, q)-Laplacian problem: {-Delta(p)u-Delta(q)u+V(epsilon x)vertical bar u vertical bar p-2u+vertical bar u vertical bar(q-2)u) = f(u) in R-N, u is an element of W-1,W-p(R-N) boolean AND W-1,W-q (R-N) where epsilon>0 is a small parameter, 1 R is a continuous function satisfying the global Rabinowitz condition, and f:R -> R is a continuous function with subcritical growth. Using suitable variational arguments and Ljusternik-Schnirelmann category theory, we investigate the relation between the number of positive solutions and the topology of the set where V attains its minimum for small epsilon.

Automated summary

This paper investigates the multiplicity and concentration of positive solutions for the (p, q)-Laplacian problem, exploring the relationship between the number of positive solutions and the topology of the set where V attains its minimum for small epsilon using variational arguments and Ljusternik-Schnirelmann category theory.