New Super-quadratic Conditions for Asymptotically Periodic Schrödinger Equations
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DOI: 10.4153/cmb-2016-090-2
Abstract: Abstract We study the semilinear Schrödinger equation $$\left\{ _{u\,\,\in \,\,{{H}^{1}}({{\mathbf{R}}^{N}}),}^{-\Delta \,u+V(x)u=f(x,u),\,\,\,\,\,x\in \,\,{{\mathbf{R}}^{N}},} \right.$$ where $f$ is a superlinear, subcritical nonlinearity. It focuses on the case where $V(x)={{V}_{0}}(x)+{{V}_{1}}(x)$ , ${{V}_{0}}\in C({{\mathbf{R}}^{N}}),\,{{V}_{0}}(x)$ is 1-periodic in each of… read more here.
Keywords: new super; conditions asymptotically; quadratic conditions; schr dinger ... See more keywords