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On the multiple spike solutions for singularly perturbed elliptic systems

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


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