Existence Of Multiple Solutions For A Class Of Kirchhoff Type Equations

In this paper,we have studied the following Kirchhoff type equation:(?)where a>0,0<b(?)1 and Ω is a bounded domain of Rn.Assume that the nonlinear term f satisfies the following (f1)f(x,u)∈C((?)×R,R),and exists c>0,r∈[1,2*),such that |f(x,u)|≤c(1+|u|r),when n=1,2,2*=+∞;when n≥3,2*=2n/(n-2);(f2)There exists constants μ≥4,M>0 satisfy 0<μF(x,u)≤uf(x,u),|u|≥M,x∈Ω;(f3)f(x,0)=0 and there exists a constant λ satisfy We prove that the above equation has at least one mountain pass solution u≠0 of this equation in W01,2(Ω).The novelty of this result is that μ=4 is allowed.