Infinitely many large energy solutions for Schrödinger-Kirchhoff type problem in \(R^N\)
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Authors
Bitao Cheng
- School of Mathematics and Information Science, Qujing Normal University, Qujing, Yunnan 655011, P. R. China.
- School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, P. R. China.
Xianhua Tang
- School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, P. R. China.
Abstract
In this paper, we consider the following Schrödinger-Kirchhoff-type problem
\[
\begin{cases}
-(a+b\int_{R^N}|\nabla u|^2 dx)\Delta u+V(x)u=g(x,u) \,\,&\hbox{for} \,\,x\in R^N,\qquad (1.1)\\
u(x)\rightarrow 0 \,\,&\hbox{as} \,\,|x|\rightarrow\infty,
\end{cases}
\]
where constants \(a > 0; b \geq 0, N = 1; 2\) or \(3, V \in C(R^N;R), g \in C(R^N \times R;R)\). Under more relaxed
assumptions on \(g(x; u)\), by using some special techniques, a new existence result of infinitely many energy
solutions is obtained via Symmetric Mountain Pass Theorem.
Share and Cite
ISRP Style
Bitao Cheng, Xianhua Tang, Infinitely many large energy solutions for Schrödinger-Kirchhoff type problem in \(R^N\), Journal of Nonlinear Sciences and Applications, 9 (2016), no. 2, 652--660
AMA Style
Cheng Bitao, Tang Xianhua, Infinitely many large energy solutions for Schrödinger-Kirchhoff type problem in \(R^N\). J. Nonlinear Sci. Appl. (2016); 9(2):652--660
Chicago/Turabian Style
Cheng, Bitao, Tang, Xianhua. "Infinitely many large energy solutions for Schrödinger-Kirchhoff type problem in \(R^N\)." Journal of Nonlinear Sciences and Applications, 9, no. 2 (2016): 652--660
Keywords
- Schrödinger-Kirchhoff type problem
- critical point
- symmetric Mountain Pass Theorem
- variational methods.
MSC
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