Quasilinear asymptotically periodic Schrödinger–Poisson system with subcritical growth
Quasilinear asymptotically periodic Schrödinger–Poisson system with subcritical growth
Abstract The aim of this paper is establishing the existence of a nontrivial solution for the following quasilinear Schrödinger–Poisson system: $$ \left \{ \textstyle\begin{array}{l} -\Delta u+V(x)u-u\Delta(u^{2})+K(x)\phi(x)u=g(x, u),\quad x\in\mathbb {R}^{3}, \\ -\Delta\phi=K(x)u^{2}, \quad x\in\mathbb{R}^{3},\\ u\in H^{1}(\mathbb{R}^{3}),\qquad u>0, \end{array}\displaystyle \right . $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mo>−</mml:mo> <mml:mi>Δ</mml:mi> <mml:mi>u</mml:mi> …