Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities

Louis Jeanjean, Kazunaga Tanaka

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We consider a class of equations of the form -ε2 Δu + V (x)u = f(u), u ∈ H1 (RN). By variational methods, we show the existence of families of positive solutions concentrating around local minima of the potential V(x), as ε → 0. We do not require uniqueness of the ground state solutions of the associated autonomous problems nor the monotonicity of the function ξ → f(ξ)/ξ. We deal with asymptotically linear as well as superlinear nonlinearities.

Original languageEnglish
Pages (from-to)287-318
Number of pages32
JournalCalculus of Variations and Partial Differential Equations
Issue number3
Publication statusPublished - 2004 Nov 1


ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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