Nonlinear Schrödinger equations without compatibility conditions on the potentials

Abstract

We study the existence of nonnegative solutions (and ground states) to the nonlinear Schrödinger equation in ${\mathbb{R}}^N$ with radial potentials and super-linear or sub-linear nonlinearities. The potentials satisfy power type estimates at the origin and at infinity, but no compatibility condition is required on their growth (or decay) rates at zero and infinity. In this respect our results extend some well known results in the literature and we also believe that they can highlight the role of the sum of Lebesgue spaces in studying nonlinear equations with weights.

19 pages, 8 figures

References in corpus (3)

• Quasilinear elliptic equations in $\RN$ via variational methods and Orlicz-Sobolev embeddings
• Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence
• Compactness and existence results in weighted Sobolev spaces of radial functions, Part I: Compactness

Cited by in corpus (6)

• Compactness and existence results for the $p$-Laplace equation
• Multiple nonradial solutions for a nonlinear elliptic problem with singular and decaying radial potential
• Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence
• Radial quasilinear elliptic problems with singular or vanishing potentials
• Compactness results for the $p$-Laplace equation
• Multiple nonradial solutions for a nonlinear elliptic radial problem: an improved result