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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 d(x,Ω) has k isolated compact connected critical sets T 1 ,,T k satisfying d(x,Ω)=c j =const., for all xT j , min ij d(T i ,T j )>2max 1jk d(T j ,Ω), and the critical group of each critical set T i is nontrivial, we construct a solution which has exactly one local maximum point in a small neighbourhood of T i , i=1,,k.
MSC:
35J65Nonlinear boundary value problems for linear elliptic equations
35B25Singular perturbations (PDE)
58E05Abstract critical point theory