On The Existence Of Solutions For Semilinear Elliptic Equation With Supercritical Nonlinearty

In this paper, we mainly consider the existence of solutions to the elliptic equations with supercritical nonlinearitywhere,Ωis a bounded smooth domain in R~N and (?)Ωdenotes the boundary ofΩ.f is a Caratheodory function and is odd about the second variable. We prove that for anyλ∈R,there exists a solution which corresponding the global minimizer of the functional; and there exists a mountain-pass solution and arbitrary many number of solutions forλlarge enough.