On a class of nonlinear elliptic equations with lower order terms. (English) Zbl 1424.35164

The authors prove existence result for weak solutions of Dirichlet problem associated to a \(p\)-Laplace operator applying Schauder’s fixed point theorem. Some difficulties occur when one tries to apply it directly, due to the presence of the first order term.
The authors begin by considering a sequence of approximated problems obtained by truncations of the gradient term and, then, by using Schauder’s fixed point theorem, under smallness assumptions on the datum and coefficient, prove that the approximated problems have weak solutions satisfying some a priori estimates.
A standard procedure of passage to the limit allows to get the existence result for the Dirichlet problem.


35J60 Nonlinear elliptic equations
35J25 Boundary value problems for second-order elliptic equations