On the multiple spike solutions for singularly perturbed ellipticsystems

Weichung Wang; Tsung-Fang Wu; Chien-Hsiang Liu

doi:10.3934/dcdsb.2013.18.237

Article Contents

2013, Volume 18, Issue 1: 237-258. Doi: 10.3934/dcdsb.2013.18.237

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On the multiple spike solutions for singularly perturbed elliptic systems

1.
Department of Mathematics, National Taiwan University, Taipei 106
2.
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811

Received: June 2011

Revised: June 2012

Published: January 2013

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Abstract

We study the multiplicity of positive solutions for the two coupled nonlinear Schrödinger equations in bounded domains in this paper. By using Nehari manifold and Lusternik-Schnirelmann category, we prove the existence of multiple positive solutions for two coupled nonlinear Schrödinger equations in bounded domains. We also propose a numerical scheme that leads to various new numerical predictions regarding the solution characteristics.

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Mathematics Subject Classification: Primary: 35J47, 35J50; Secondary: 35J57.

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References

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