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On Anisotropic Elliptic Equations in Bounded Domains
Abstract
Because of the anisotropic character of the equations in (Qc) and (Pc) below, in solving those problems, we cannot right away apply the comparison principles. We will pick up some conditions under which the existence of some sub-and-super solutions of the problems leads to the existence theorems for those problems.
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We consider the model problem Δu=f(u)+g(u),u>0,x∈Ω,u| ∂Ω =∞, where f(u)=e u , -C 3 e s <g(s)≤C 4 <2λ 1 , s≥0; or f(u)=u p (p>1), -C 5 s p ≤g(s)≤C 6 s 1+1 p , s≥0. We prove that there exists a solution u∈C 2+α (Ω), where C 3 ,C 4 ,C 5 ,C 6 are positive constants with C 5 ,C 3 ∈(0,1).