Nonexistence and existence of positive radial solutions to a class of quasilinear Schrödinger equations in $\mathbb{R}^{N}$,Boundary Value Problems

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Nonexistence and existence of positive radial solutions to a class of quasilinear Schrödinger equations in $\mathbb{R}^{N}$
Boundary Value Problems ( IF 1.0 ) Pub Date : 2020-04-28 , DOI: 10.1186/s13661-020-01378-5
Jing Li , Ying Wang

This paper aims to investigate the class of quasilinear Schrödinger equations 0.1 $$\begin{aligned} \begin{aligned}[b] &-\Delta u-\bigl[\Delta \bigl(1+u^{2}\bigr)^{\frac{\gamma }{2}}\bigr] \frac{\gamma u}{2(1+u^{2})^{\frac{2-\gamma }{2}}}\\ &\quad =\alpha h\bigl( \vert x \vert \bigr) \vert u \vert ^{p-1}u+ \beta H\bigl( \vert x \vert \bigr) \vert u \vert ^{q-1}u, \quad x\in \mathbb{R}^{N}, \end{aligned} \end{aligned}$$ where $N >2$, $1 \le \gamma \le 2$, $\alpha ,\beta \in \mathbb{R}$ and either $0< p<1

中文翻译：

\（\ mathbb {R} ^ {N} \）中一类拟线性Schrödinger方程的不存在和正径向解的存在

本文旨在研究拟线性Schrödinger方程的类别0.1 $$ \ begin {aligned} \ begin {aligned} [b]＆-\ Delta u- \ bigl [\ Delta \ bigl（1 + u ^ {2} \ bigr ）^ {\ frac {\ gamma} {2}} \ bigr] \ frac {\ gamma u} {2（1 + u ^ {2}）^ {\ frac {2- \ gamma} {2}}} \\ \＆\ quad = \ alpha h \ bigl（\ vert x \ vert \ bigr）\ vert u \ vert ^ {p-1} u + \ beta H \ bigl（\ vert x \ vert \ bigr）\ vert u \ vert ^ {q-1} u，\ quad x \ in \ mathbb {R} ^ {N}，\ end {aligned} \ end {aligned} $$其中$ N> 2 $，$ 1 \ le \ gamma \ le 2 $，$ \ alpha，\ beta \ in \ mathbb {R} $和$ 0 <p <1

更新日期：2020-04-28

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