Electron. J. Differential Equations, Vol. 2018 (2018), No. 109, pp. 1-12.

Steady-state solutions for Schrodinger equations in photonic lattice

Wen-Long Li

In this article, we study a nonlinear Schrodinger equation arising in optics. Firstly we prove the existence of multiple solutions of this equation. Secondly, we consider a nonlinear Schrodinger system which is intimately related to the Schrodinger equation. We obtain the existence of nontrivial solutions to this system and we also get some results on its positive solutions. Finally, assuming Dirichlet or Neumann boundary condition, we show the existence and uniqueness of positive solution to the Schrodinger equation.

Submitted July 18, 2017. Published May 8, 2018.
Math Subject Classifications: 35J20, 35B09, 35J47.
Key Words: Schrodinger equation; multiple solutions; positive solution; nontrivial solution.

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Wen-Long Li
Department of Mathematics
Nanjing University
Nanjing 210093, China
email: liwenlongchn@gmail.com

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