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

AbstractIn 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⊂RN is a bounded domain, N⩾1 andAu=−∑i,j=1NDi[aij(x)Dju]+c(x)u, aij(x)=aji(x)∈c1(Ω¯), i,j=1,2,…,N, c(x)∈C(Ω¯), c(x)⩾0 and there is γ>0 such that∑i,j=1Naij(x)ξiξj⩾γ|ξ|2,∀x∈Ω¯,ξ∈RN