Quasilinear Elliptic Equations Characteristic Value Problems

In this paper, we study the multiplicity results of solutions for a quasilinear elliptic eigenvalue problem, by using minimax methods from critical point theory. Consider the quasilinear elliptic eigenvalue problemwhere Ω (?) R^N is a bounded domain with smooth boundary (?)Ω, â–³_pu = div(|â–½_u|^p-2â–½_u)is the p-Laplacian operator. We impose the function f on condition as follows.(F) f ∈ C(R,R) and (?) where 1＜p＜q＜p* Let N(λ) be the number of solutions of problem (Pλ).Our main results in this paper is the following theorem. Theorem Assume that (F) is satisfied. Then N(λ)â†'∞, as λ â†' ∞.