Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations
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Authors
Xiujuan Wang
- School of Mathematical Sciences, Qufu Normal University, Shandong 273165, P. R. China.
Aixia Qian
- School of Mathematical Sciences, Qufu Normal University, Shandong 273165, P. R. China.
Abstract
This paper focuses on the following elliptic equation
\[
\left\{ \begin{aligned}
-u''- p(x)u=f(x,u),\quad \text{a.e.}\quad x\in[0,l],\\
u(0)-u(l)=u'(0)-u'(l)=0,
\end{aligned} \right. \]
where the primitive function of \(f(x,u)\) is either superquadratic or asymptotically quadratic as \(|u|\rightarrow\infty\), or subquadratic as \(|u|\rightarrow0\). By using variational method, e.g. the local linking theorem, fountain theorem, and the generalized mountain pass theorem, we establish the existence and multiplicity results for the periodic solution and subharmonic solution.
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ISRP Style
Xiujuan Wang, Aixia Qian, Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 12, 6229--6245
AMA Style
Wang Xiujuan, Qian Aixia, Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations. J. Nonlinear Sci. Appl. (2017); 10(12):6229--6245
Chicago/Turabian Style
Wang, Xiujuan, Qian, Aixia. "Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations." Journal of Nonlinear Sciences and Applications, 10, no. 12 (2017): 6229--6245
Keywords
- Elliptic equation
- periodic solution
- superquadratic
- subquadratic
- asymptotically quadratic
- subharmonic solution
MSC
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