Effect of the domain geometry on the existence of multipeak solutions for an elliptic problem. (English) Zbl 0958.35054
Summary: We construct multipeak solutions for a singularly perturbed Dirichlet problem. Under the conditions that the distance function has isolated compact connected critical sets satisfying , for all , , and the critical group of each critical set is nontrivial, we construct a solution which has exactly one local maximum point in a small neighbourhood of , .
|35J65||Nonlinear boundary value problems for linear elliptic equations|
|35B25||Singular perturbations (PDE)|
|58E05||Abstract critical point theory|