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Search: authors:"Liqian Jia"

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Discrete Schrödinger equations in the nonperiodic and superlinear cases: homoclinic solutions

Using variational methods, we study the existence and multiplicity of homoclinic solutions for a class of discrete Schrödinger equations in infinite m-dimensional lattices with nonlinearities being superlinear at infinity. Our results generalize some existing results in the literature by using some weaker conditions.

Multiple solutions of discrete Schrödinger equations with growing potentials

Under some weaker conditions than elsewhere, we obtain infinitely many homoclinic solutions for a class of discrete Schrödinger equations in infinite m dimensional lattices with nonlinearities being superlinear at infinity by using variational methods. Our result extends some existing results in the literature. MSC: 35Q51, 35Q55, 39A12, 39A70.