Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials

By Yanheng Ding, Jun-cheng Wei. 2007

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We establish the existence and multiplicity of semiclassical bound states of the following nonlinear Schrodinger equation: {−e2Δu+V(x)u=g(x,u)for x∈RN,u(x)→0as |x|→∞ where V changes sign and g is superlinear with critical or supercritical growth as |u|→∞.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/10be3b319938b20ed315167066f1c3ae386838a6