论文标题
在平面Schrödinger-Poisson系统上，涉及非对称电势
On a planar Schrödinger-Poisson system involving a non-symmetric potential
论文作者
论文摘要
我们证明了Schrödinger-Poisson Systems在形式的平面中存在基态阳性解决方案 $ - Δu + v（x）u + \fracγ{2π} \ left（\ log | \ cdot | \ ast u^2 \ right）和无限无限。在潜力上，我们不需要任何对称性或周期性假设，也不需要它在无穷大时具有限制。我们使用Mountain Pass定理和Cerami紧凑条件的变体来解决问题。
We prove the existence of a ground state positive solution of Schrödinger-Poisson systems in the plane of the form $$ -Δu + V(x)u + \fracγ{2π} \left(\log|\cdot| \ast u^2 \right)u = b |u|^{p-2}u \qquad\text{in}\ \mathbb{R}^2, $$ where $p>4$, $γ,b>0$ and the potential $V$ is assumed to be positive and unbounded at infinity. On the potential we do not require any symmetry or periodicity assumption, and it is not supposed it has a limit at infinity. We approach the problem by variational methods, using a variant of the mountain pass theorem and the Cerami compactness condition.
