Leray Lions degenerated problem with general growth condition

Abstract

In this paper, we study the existence of solutions for the nonlinear degenerated elliptic problem $$ -{mathop{ m div}}(a(x,u, abla u)) = Fquad mbox{in } Omega, $$ where $Omega$ is a bounded domain of $mathbb{R}^N$, $N geq 2$, $a:Omegaimesmathbb{R}imesmathbb{R}^Nomathbb{R}^N $ is a Caratheodory function satisfying the coercivity condition, but they verify the general growth condition and only the large monotonicity. The second term $F$ belongs to $W^{-1, p'}(Omega, w^*)$.

Keywords

• Weighted Sobolev spaces
• truncations
• $L^1$-version of Minty's lemma
• Hardy inequality.