Boundary concentration phenomena for a singularly perturbed elliptic problem

Communications on Pure and Applied Mathematics - Tập 55 Số 12 - Trang 1507-1568 - 2002
Andrea Malchiodi1, Marcelo Montenegro2
1Institute for Advanced Study, School of Mathematics, 1 Einstein Drive, Princeton, NJ 08540
2Universidade Estadual de Campinas, Departamento de Matem�tica, Caixa Postal 6065, CEP 13083‐970, Campinas, SP, Brazil

Tóm tắt

AbstractWe exhibit new concentration phenomena for the equation − ε2 Δu + u = up in a smooth bounded domain Ω ⊆ ℝ2 and with Neumann boundary conditions. The exponent p is greater than or equal to 2 and the parameter ε is converging to 0. For a suitable sequence εn → 0 we prove the existence of positive solutions un concentrating at the whole boundary of Ω or at some component. © 2002 Wiley Periodicals, Inc.

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