Double phase problems with competing potentials: concentration and multiplication of ground states

摘要

In this paper, we establish concentration and multiplicity properties of ground state solutions to the following perturbed double phase problem with competing potentials: {-epsilon(p )Delta p(u) - epsilon(q )Delta(q)u + V(x)(vertical bar u vertical bar(p-2 )u + vertical bar u vertical bar(q-2)u) = K (x) f (u), in R-N, u is an element of W-1,W-p (R-N) boolean AND W-1,W-q (R-N), u > 0, in R-N, where 1 0. The asymptotic convergence and the exponential decay of positive solutions are also explored. Finally, we establish a sufficient condition for the non-existence of ground state solutions.