论文标题
具有潜力的质量超临界schrödinger方程的归一化解决方案
Normalized solutions of mass supercritical Schrödinger equations with potential
论文作者
论文摘要
本文涉及非线性schrödinger方程的归一化解决方案\ [ -ΔU+v（x）u+λu= | u |^{p-2} u \ qquad \ text {in $ \ mathbb {r}^n $} \]在质量超临界和sobolev subolev sublitical case $ 2+\ frac {4} {4} {n} {n} {n} <p <2^*$。我们证明了解决方案的存在$（u，λ）\在h^1（\ Mathbb {r}^n）\ times \ times \ times \ times \ mathbb {r}^+$带有规定的$ l^2 $ -norm $ -norm $ \ | | U \ | U \ | _2 =ρ=ρ$在电位$ v的各种条件下，在无穷大的消失，包括具有奇异性的潜力。证明是基于新的Min-Max参数。
This paper is concerned with the existence of normalized solutions of the nonlinear Schrödinger equation \[ -Δu+V(x)u+λu = |u|^{p-2}u \qquad\text{in $\mathbb{R}^N$} \] in the mass supercritical and Sobolev subcritical case $2+\frac{4}{N}<p<2^*$. We prove the existence of a solution $(u,λ)\in H^1(\mathbb{R}^N)\times\mathbb{R}^+$ with prescribed $L^2$-norm $\|u\|_2=ρ$ under various conditions on the potential $V:\mathbb{R}^N\to\mathbb{R}$, positive and vanishing at infinity, including potentials with singularities. The proof is based on a new min-max argument.
