Nontrivial solution for Schrödinger-Poisson equations involving a fractional nonlocal operator via perturbation methods
From the abstract: ''This paper focuses on the following Schrödinger-Poisson equations involving a fractional nonlocal operator \[ \begin{cases} -\Delta u + u + \phi u = f(x, u),\quad &\text{in }\mathbb{R}^3,\\ (-\Delta)^{\alpha/2}\phi = u^2, \quad&\text{in }\mathbb{R}^3, \\ \, \lim_{|x|\to\infty}\phi(x) = 0, \end{cases} \] where \(\alpha \in (1,2]\). Under certain assumptions, we obtain the existence of nontrivial solution of the above problem without compactness by using the methods of perturbation and the mountain pass theorem.''
scientific article; zbMATH DE number 6639267
scientific article