Multi-peak solutions for a singularly perturbed semilinear elliptic problem

[摘要] This paper is concerned with the existence of multi-peak solutions of the following problem -epsilon(2)Delta u + u = u(p-1) in Omega, u > 0 in Omega, u = 0 on theta Omega, -where SZ is a smooth bounded domain in R-N (N greater than or equal to 2), epsilon > 0 is a small positive number and p epsilon (2, 2N/N-2) for N greater than or equal to 3, p epsilon (2, + infinity) for N = 2. Using a variational method we construct positive solutions concentrating near given saddle points of the distance function dist(., theta Omega). An explicit expression for the dominant parts of the solutions is also obtained. (C) 2000 Academic Press.

[发布日期] 2000-09-20