# American Institute of Mathematical Sciences

May  2007, 19(2): 255-269. doi: 10.3934/dcds.2007.19.255

## Multi-peak standing waves for nonlinear Schrödinger equations with a general nonlinearity

 1 Department of Mathematics, Pohang University of Science and Technology, Pohang, Kyungbuk 790-784, South Korea 2 Equipe de Mathématiques (UMR CNRS 6623), Université de Franche-Comté, 16 Route de Gray, 25030 Besançon

Received  September 2005 Revised  October 2005 Published  July 2007

We consider singularly perturbed elliptic equations $\varepsilon^2\Delta u - V(x) u + f(u)=0, x\in R^N, N \ge 3.$ For small $\varepsilon > 0,$ we glue together localized bound state solutions concentrating at isolated components of positive local minimum of $V$ under conditions on $f$ we believe to be almost optimal.
Citation: Jaeyoung Byeon, Louis Jeanjean. Multi-peak standing waves for nonlinear Schrödinger equations with a general nonlinearity. Discrete & Continuous Dynamical Systems, 2007, 19 (2) : 255-269. doi: 10.3934/dcds.2007.19.255
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