# Boundary Value Problems

Boundary Value Problems > 2019 > 2019 > 1 > 1-15

Boundary Value Problems > 2019 > 2019 > 1 > 1-16

*x*. By using the non-Nehari...

Boundary Value Problems > 2019 > 2019 > 1 > 1-15

We are concerned with the following Schrödinger–Poisson system: {−Δu+u+K(x)ϕu=a(x)u3,x∈R3,−Δϕ=K(x)u2,x∈R3. $$ \textstyle\begin{cases} -\Delta u+u+K(x)\phi u=a(x)u^{3},& x\in \mathbb{R}^{3}, \\ -\Delta \phi =K(x)u^{2}, & x\in \mathbb{R}^{3}. \end{cases} $$ Assuming that K(x) $K(x)$ and a(x) $a(x)$ are nonnegative functions satisfying lim|x|→∞a(x)=a∞>0,lim|x|→∞K(x)=0, $$ \lim_{|x|\rightarrow...

Boundary Value Problems > 2019 > 2019 > 1 > 1-16

This paper is dedicated to studying the following Schrödinger–Poisson system: {−△u+V(x)u+K(x)ϕ(x)u=f(x,u),x∈R3,−△ϕ=K(x)u2,x∈R3, $$ \textstyle\begin{cases} -\triangle u+V(x)u+K(x)\phi (x)u=f(x, u), \quad x\in {\mathbb {R}}^{3}, \\ -\triangle \phi =K(x)u^{2}, \quad x\in {\mathbb {R}}^{3}, \end{cases} $$ where V(x) $V(x)$, K(x) $K(x)$, and f(x,u) $f(x, u)$ are periodic in *x*. By using the non-Nehari...