文章基本信息

标题：RETRACTED ARTICLE: Sign-changing solutions to Schrödinger-Kirchhoff-type equations with critical exponent
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作者：Liping Xu ; Haibo Chen
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2016
卷号：2016
期号：1
页码：176
DOI：10.1186/s13662-016-0864-9
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study the following Schrödinger-Kirchhoff-type equation: { − ( a + b ∫ R 3 ∇ u 2 d x ) △ u + u = k ( x ) u 2 ∗ − 2 u + μ h ( x ) u in R 3 , u ∈ H 1 ( R 3 ) , $$ \textstyle\begin{cases} -(a+b\int_{\mathrm{R}^"} \nabla u ^,\,dx)\triangle u+u= k(x) u ^{2^{*}-2}u+\mu h(x)u \quad \text{in } \mathrm{R}^", \\ u\in H^)(\mathrm{R}^"), \end{cases} $$ where a , b , μ > 0 $a, b, \mu>0$ are constants, 2 ∗ = 6 $2^{*}=6$ is the critical Sobolev exponent in three spatial dimensions. Under appropriate assumptions on nonnegative functions k ( x ) $k(x)$ and h ( x ) $h(x)$ , we establish the existence of positive and sign-changing solutions by variational methods.
关键词：Schrödinger-Kirchhoff-type equations ; critical nonlinearity ; positive solutions ; sign-changing solutions ; variational methods