期刊论文

Multiple Solutions for Nonlinear Equations Related to Kirchhoff Type Equations

中文

数学物理学报

1003-3998

2020

40

04

842-849

10.3969/j.issn.1003-3998.2020.04.002

11071095:国家自然科学基金 11371159:国家自然科学基金

本校为第一机构

该文研究如下Kirchhoff型方程$$\left\{ \begin{array}{l} - \left( {a + b\int_{{R^3}} {{{\left| {\nabla u} \right|}^2}} } \right)\Delta u + u = \left( {1 + \varepsilon g\left( x \right)} \right){u^p},x \in {{\rm\mathbb{R}}^3},\\u \in {H^1}\left( {{{\rm\mathbb{R}}^3}} \right)\end{array} \right.$$其中$\varepsilon,a,b$都是正常数,$1 < p < 5,g\left( x \right) \in {L^\infty }\left( {{{\rm\mathbb{R}}^3}} \right)$.应用扰动的方法证明了:对于适当的$g\left( x \right)$,存在${\varepsilon _0}$,当$0 < \varepsilon < {\varepsilon _0}$时,...

In this paper, we will discuss the following Kirchhoff equation $$\left\{ {\begin{array}{*{20}{l}}{ - \left( {a + b\int_{{{\rm\mathbb{R}}^3}} {{{\left| {\nabla u} \right|}^2}} } \right)\Delta u + u = \left( {1 + \varepsilon g\left( x \right)} \right){u^p},x \in {{\rm\mathbb{R}}^3},}\\{u \in {H^1}\left( {{{\rm\mathbb{R}}^3}} \right)}\end{array}} \right.$$, where $\varepsilon,a,b$ are positive constants, $1 < p < 5,g\left( x \right) \in {L^\infty }\left( {{{\rm\mathbb{R}}^3}} \right)$.When $g\left( x \right)$satisfy some conditions, we use perturbation method prove that there exists a ${\varepsi...