Existence results for nonlinear elliptic equations (Q1851415)

Existence results are proved for the problem \(Au+g(x,u,Du)+H(x,Du)=f\), \(u\in W^{1,p}_0 (\Omega)\) where \(\Omega\) is a bounded set, \(A\) is a Leray-Lions operator; the function \(g(x,u,t)\) is a nonlinear lower-order term having \(p\)-growth \((p>1)\) in \(t\) and satisfies a sign condition with respect to \(u\), while the function \(H(x,t)\) grows at most as \(|t|^{p-1}\). A priori estimates for the solution are obtained using symmetrization techniques. Then a sequence of approximate problems is considered and a priori estimates are found. This allows to pass to the limit in the sequence of approximate problems.