Infinitely many solutions for a class of fractional Schrodinger equations coupled with neutral scalar field
Abstract
We study the fractional Schrödinger equations coupled with a neutral scalar field $$ (-\Delta)^s u+V(x)u=K(x)\phi u +g(x)|u|^{q-2}u, \quad x\in \mathbb{R}^3,\qquad (I-\Delta)^t \phi=K(x)u^2, \quad x\in \mathbb{R}^3, $$ where $(-\Delta)^s$ and $(I-\Delta)^t$ denote the fractional Laplacian and Bessel operators with $\frac{3}{4} <s<1$ and $0<t<1$, respectively. Under some suitable assumptions for the external potentials $V$, $K$ and $g$, given $q\in(1,2)\cup(2,2_s^*)$ with $2_s^*:= \frac{6}{3-2s}$, with the help of an improved Fountain theorem dealing with a class of strongly indefinite variational problems approached by Gu-Zhou [Adv. Nonlinear Stud., {\bf 17} (2017), 727--738], we show that the system admits infinitely many nontrivial solutions.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2024
- DOI:
- 10.48550/arXiv.2402.12006
- arXiv:
- arXiv:2402.12006
- Bibcode:
- 2024arXiv240212006S
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35J60;
- 35Q55;
- 53C35
- E-Print:
- 15 pages