Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory

We study a perturbed semilinear problem with Neumann boundary condition [GRAPHICS] where Omega is a bounded smooth domain of R-N, N greater than or equal to 2, epsilon > 0, 1 < p < N+2/N-2 if N greater than or equal to 3 or p > I if N = 2 and v is the unit outward normal at the boundary of Omega. We show that for any fixed positive integer K any "suitable" critical point (x(0)(1),..., x(0)(K)) of the function rK(x(1),...,x(K)) = min {dist(x(i),partial derivative Omega), \x(j)-x(l)/2 \i, j, l = 1..., K, j not equal l} generates a family of multiple interior spike solutions, whose local maximum points x1 epsilon,..., xK epsilon tend to x(0)(1) as epsilon tends to zero. Mathematics Subject Classification (1991):35J40.