A Minimax Inequality for a Class of Functionals and Its Applications to Existence of Multiple Solutions for Elliptic Equations
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Authors
M. Khaleghi Moghadam
- Department of Basic Sciences, Faculty of Agriculture Engineering, Sari Agricultural Sciences and Natural Resources University, P. O. Box 578 Sari, Iran
G. A. Afrouzi
- Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran
J. Vahidi
- Department of Applied Mathematics, Iran University of Science and Technology, Behshahr, Iran
Abstract
In this paper, we establish an equivalent statement of minimax inequality for a special
class of functionals. As an application, we discuss the existence of three solutions to the
Dirichlet problem \[
\begin{cases}
\Delta_{p}u=\lambda f(x,u)=a(x)|u|^{p-2}u,\,\,\,\,\, \texttt{in} \Omega,\\
u=0,\,\,\,\,\, \texttt{on} \partial \Omega.
\end{cases}
\]
Share and Cite
ISRP Style
M. Khaleghi Moghadam, G. A. Afrouzi, J. Vahidi, A Minimax Inequality for a Class of Functionals and Its Applications to Existence of Multiple Solutions for Elliptic Equations, Journal of Mathematics and Computer Science, 4 (2012), no. 3, 350--360
AMA Style
Khaleghi Moghadam M., Afrouzi G. A., Vahidi J., A Minimax Inequality for a Class of Functionals and Its Applications to Existence of Multiple Solutions for Elliptic Equations. J Math Comput SCI-JM. (2012); 4(3):350--360
Chicago/Turabian Style
Khaleghi Moghadam, M., Afrouzi, G. A., Vahidi, J.. "A Minimax Inequality for a Class of Functionals and Its Applications to Existence of Multiple Solutions for Elliptic Equations." Journal of Mathematics and Computer Science, 4, no. 3 (2012): 350--360
Keywords
- Minimax inequality
- Critical point
- Three solutions
- Multiplicity results
- Dirichlet problem.
MSC
- 49J35
- 34B15
- 34B09
- 35J57
- 35J92
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