On a class of singularly perturbed elliptic equations in divergence form: existence and multiplicity results

[摘要] The main purpose of this paper is to study the existence of single-peaked positive solutions of the singularly perturbed elliptic equation -epsilon(2)div(J(x)Deltau) + V(x)u = f (u) in R-N, where J is a symmetric uniformly elliptic matrix and V is a positive potential, possibly unbounded from above. If f(u) = u(P), then solutions concentrate at non-degenerate critical points of Gamma(x) = V(x) p+1/p-1 - N/2 (det J(x))1/2. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-15

[关键词] singularly perturbed elliptic PDEs;concentrating solutions