论文标题
一类局部超级线性schrödinger方程的阳性解决方案的存在和渐近行为
Existence and asymptotic behavior of positive solutions for a class of locally superlinear Schrödinger equation
论文作者
论文摘要
本文将$-ΔU + v（x）u =λf（u）$ in $ \ mathbb {r}^n $中的阳性解决方案的存在。这里$ n \ geq 1 $，$λ> 0 $是参数，$ f（u）$仅在$ u = 0 $的附近满足条件。我们将展示具有诱捕类型的潜在或$ \ Mathcal {g} $ - 对称潜力的积极解决方案的存在，其中$ \ MATHCAL {G} \ subset O（n）$。我们的结果扩展了先前的结果，并且我们还研究了一个家庭$（u_λ）_ {λ\geqλ_0} $的渐近行为，为$λ\ to \ infty $。
This paper treats the existence of positive solutions of $-Δu + V(x) u = λf(u)$ in $\mathbb{R}^N$. Here $N \geq 1$, $λ> 0$ is a parameter and $f(u)$ satisfies conditions only in a neighborhood of $u=0$. We shall show the existence of positive solutions with potential of trapping type or $\mathcal{G}$-symmetric potential where $\mathcal{G} \subset O(N)$. Our results extend previous results as well as we also study the asymptotic behavior of a family $(u_λ)_{λ\geq λ_0}$ of positive solutions as $λ\to \infty$.
