Dirichlet (p,q)-equations with gradient dependent and locally defined reaction

Abstract

We consider a Dirichlet (p,q)-equation, with a gradient dependent reaction which is only locally defined. Using truncations, theory of nonlinear operators of monotone type, and fixed point theory (the Leray-Schauder Alternative Theorem), we show the existence of a positive smooth solution.
 For more information see https://ejde.math.txstate.edu/Volumes/2021/34/abstr.html