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arXiv · 2308.02311

Compact embeddings for weighted fractional Sobolev spaces and applications to Nonlinear Schr\"odinger Equations

Federico Bernini·Sergio Rolando·Simone Secchi
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Abstract

The aim of this work is to prove a compact embedding for a weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the existence of solutions for the following Schr\"odinger equation $$ (-\Delta)^su + V(|x|)u = K(|x|)f(u), \quad \text{ in } \mathbb{R}^N, $$ where the two measurable functions $K > 0$ and $V \geq 0$ could vanish at infinity.

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Federico Bernini, Sergio Rolando, Simone Secchi. 2023-08-04. Compact embeddings for weighted fractional Sobolev spaces and applications to Nonlinear Schr\"odinger Equations. https://arxiv.org/abs/2308.02311

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