Electronic Journal of Differential Equations, Vol. 1993(1993), No. 05, pp. 1-21.

Title: Least-energy Solutions to a non-autonomous semilinear 
       problem with small diffusion coefficient

Authors: Xiaofeng Ren (Univ. of Minnesota, Minneapolis, MN)

Abstract: Least-energy solutions of a non-autonomous semilinear 
problem with a small diffusion coefficient are studied in this paper.
We prove that the solutions will develop single peaks as the 
diffusion coefficient approaches 0. The location of the peaks is 
also considered in this paper. It turns out that the location of the
peaks is determined by the non-autonomous term of the equation and 
the type of the boundary condition. Our results are based on fine 
estimates of the energies of the solutions and some non-existence 
results for semilinear equations on half spaces with Dirichlet 
boundary condition and some decay conditions at infinity.

Submitted August 19, 1993. Published October 15, 1993.
Math Subject Classification: 35B25, 35B40.
Key Words: Least-energy solution; Spiky pattern.