Abstract:We study the existence of solutions of the following nonlinear Schrödinger equation $$ -\Delta u+V(x)u-\frac{(N-2)^2}{4|x|^2}u=f(x,u) $$ where $V:\mathbb{R}^N\to\mathbb{R}$ and $f:\mathbb{R}^N\times \mathbb{R}\to \mathbb{R}$ are periodic with respect to $x\in\mathbb{R}^N.$ We assume that $V$ has positive essential infimum, $f$ satisfies weak growth conditions and $N\geq 3$. The approach to the problem uses variational methods with nonstandard functional setting. We obtain the existence of the ground state solution using the new profile decomposition.
| Subjects: | Analysis of PDEs (math.AP) |
| MSC classes: | 35Q60, 35Q55, 35A15, 35J20, 58E05 |
| Cite as: | arXiv:2602.16524 [math.AP] |
| (or arXiv:2602.16524v2 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2602.16524 arXiv-issued DOI via DataCite |
From: Bartosz Bieganowski Dr [view email]
[v1]
Wed, 18 Feb 2026 15:11:37 UTC (14 KB)
[v2]
Tue, 26 May 2026 13:46:00 UTC (14 KB)
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