论文标题
一类非线性Schrödinger-Poisson系统的地面和无限的许多高能源解决方案
Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger-Poisson systems
论文作者
论文摘要
我们研究了一个非线性schrödinger-poisson系统，该系统还原为非线性和非局部方程\ [ - ΔU + u + u +λ^2 \ left（\ frac {1} {ω| x | x | x |^{n-2}}} \ starρu^2 \ right） r^n，\]其中$ω=（n-2）| \ mathbb {s}^{n-1} |，$ $ c = 0，$ $ q \ in（2,2,2^{\ ast} -1），$ $ $ρ：\ mathbb r^n \ to \ to \ to \ to \ to \ to \ to \ nathbb r $ co \ mathbb r $是$ and $ ny andly and n n = 3，$ n = 3,4 $ 2^*= 2n/（n-2）$是关键的Sobolev指数。我们证明了在合适的有限能量空间上工作的解决方案的存在和多样性，在两个单独的假设下，这些假设与可能发生紧凑现象丧失的情况兼容。
We study a nonlinear Schrödinger-Poisson system which reduces to the nonlinear and nonlocal equation \[- Δu+ u + λ^2 \left(\frac{1}{ω|x|^{N-2}}\star ρu^2\right) ρ(x) u = |u|^{q-1} u \quad x \in \mathbb R^N, \] where $ω= (N-2)|\mathbb{S}^{N-1}|,$ $λ>0,$ $q\in(2,2^{\ast} -1),$ $ρ:\mathbb R^N \to \mathbb R$ is nonnegative and locally bounded, $N=3,4,5$ and $2^*=2N/(N-2)$ is the critical Sobolev exponent. We prove existence and multiplicity of solutions working on a suitable finite energy space and under two separate assumptions which are compatible with instances where loss of compactness phenomena may occur.
