Positive solutions of Schrodinger-Poisson systems with Hardy potential and indefinite nonlinearity

Abstract

In this article, we study the nonlinear Schrodinger-Poisson system $$\displaylines{ -\Delta u+u-\mu\frac{u}{|x|^2}+l(x) \phi u=k(x)|u|^{p-2}u \quad x\in\mathbb{R}^3, \cr -\Delta\phi=l(x)u^2 \quad x\in\mathbb{R}^3, }$$ where \(k\in C(\mathbb{R}^3)\) and 4<p<6, k changes sign in \(\mathbb{R}^3\) and \(\limsup_{|x|\to\infty}k(x)=k_{\infty}<0\). We prove that Schrodinger-Poisson systems with Hardy potential and indefinite nonlinearity have at least one positive solution, using variational methods. For more information see https://ejde.math.txstate.edu/Volumes/2020/47/abstr.html