On multiplicity of solutions of Dirichlet problem for uniformly elliptic operator equations

In the present paper, the following Dirichlet problem{A(u)=f(x,u),in Ω,u=0,on ∂Ω, is studied and four new multiplicity results of solutions are obtained, where Ω⊂RNΩ⊂RN is a bounded domain, N⩾1N⩾1 andAu=−∑i,j=1NDi[aij(x)Dju]+c(x)u,aij(x)=aji(x)∈c1(Ω¯), i,j=1,2,…,Ni,j=1,2,…,N, c(x)∈C(Ω¯), c(x)⩾0c(x)⩾0 and there is γ>0γ>0 such that∑i,j=1Naij(x)ξiξj⩾γ|ξ|2,∀x∈Ω¯,ξ∈RN.