The Existence And Concentration Of Bound-state Solutions To A Class Of P-Laplacian Type Elliptic Problems In Unbounded Domains

In this paper, we study the existence of bound-state solution for the p-Laplacian type equation where Ω is a domain in RN, possibly unbounded, with empty or smooth boundary. ε is a small positive parameter,f∈C1(R+, R), with a subcritical, super (p—1) th power of growth, V:RN→R is a locally Holder continuous function which is bounded from below, away from zero, such that for some open bounded subset A of Ω. We prove that there is an ε0>0such that for any ε∈(0,ε0], the above mentioned problem possesses a bound-state weak solution with exponential decay. The proof of this result is variational, mainly based on the penalty method and the Mountain Pass Theorem. Our result generalizes a similar result in [13] for semilinear elliptic equations to p-Laplacian type problem.