A Minimax Inequality For A Class Of Functionals And Its Applications To Existence Of Multiple Solutions For Elliptic Equations

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