Li, Wen-Long2022-02-022022-02-022018-05-08Li, W. L. (2018). Steady-state solutions for Schrödinger equations in photonic lattice. <i>Electronic Journal of Differential Equations, 2018</i>(109), pp. 1-12.1072-6691https://hdl.handle.net/10877/15276In this article, we study a nonlinear Schrödinger equation arising in optics. Firstly we prove the existence of multiple solutions of this equation. Secondly, we consider a nonlinear Schrödinger system which is intimately related to the Schrödinger 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 Schrödinger equation.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalSchrödinger equationMultiple solutionsPositive solutionsNontrivial solutionsArticle