Existence results for a class of nonlinear elliptic problems with p-growth in the gradient

Abstract

We prove the existence of bounded solutions for a class of nonlinear elliptic problems whose model is in the form: (∗) − div(a(x,u,Du))=k 1(|u|)|Du| p+k 2(|u|)f,u∈W 0 1,p(Ω)∩L ∞(Ω), where 〈 a( x, η, ξ) ξ〉⩾ b(| η|)| ξ| p , b is a continuous monotone decreasing function and k 1 and k 2 are continuous monotone increasing functions.