A Minimax Inequality for a Class of Functionals and Its Applications to Existence of Multiple Solutions for Elliptic Equations


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


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 \[ \begin{cases} \Delta_{p}u=\lambda f(x,u)=a(x)|u|^{p-2}u,\,\,\,\,\, \texttt{in} \Omega,\\ u=0,\,\,\,\,\, \texttt{on} \partial \Omega. \end{cases} \]