Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities

Louis Jeanjean*, Kazunaga Tanaka

*この研究の対応する著者

研究成果: Article査読

152 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)287-318
ページ数32
ジャーナルCalculus of Variations and Partial Differential Equations
21
3
DOI
出版ステータスPublished - 2004 11月

ASJC Scopus subject areas

  • 分析
  • 応用数学

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