Ground state solutions for a non-local type problem in fractional Orlicz Sobolev spaces
Abstract
In this paper, we study the following nonlocal problem in fractional Orlicz Sobolev spaces \begin{eqnarray*} (-\Delta_{\Phi})^{s}u+V(x)a(|u|)u=f(x,u),\quad x\in\mathbb{R}^N, \end{eqnarray*} where $(-\Delta_{\Phi})^{s}(s\in(0, 1))$ denotes the non-local and maybe non-homogeneous operator, the so-called fractional $\Phi$-Laplacian. Without assuming the Ambrosetti-Rabinowitz type and the Nehari type conditions on the nonlinearity, we obtain the existence of ground state solutions for the above problem in periodic case. The proof is based on a variant version of the mountain pass theorem and a Lions' type result for fractional Orlicz Sobolev spaces.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2023
- DOI:
- 10.48550/arXiv.2311.08905
- arXiv:
- arXiv:2311.08905
- Bibcode:
- 2023arXiv231108905W
- Keywords:
-
- Mathematics - Analysis of PDEs