Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities

被引：0

作者：

Jeanjean L. ^{[1
]}

Tanaka K. ^{[2
]}

机构：

[1] Equipe de Mathématiques, UMR CNRS 6623, Universite de Franche-Comte, 25030 Besançon

[2] Department of Mathematics, School of Science and Engineering, Waseda University, Shinjuku-ku, Tokyo 169-8555

来源：

Calculus of Variations and Partial Differential Equations | 2004年 / 21卷 / 3期

关键词：

Local Minimum; State Solution; Variational Method; Potential Versus; Elliptic Problem;

D O I：

10.1007/s00526-003-0261-6

中图分类号：

学科分类号：

摘要：

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.

引用

页码：287 / 318

页数：31

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