Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 34, pp. 1-8.

Title: Dirichlet (p,q)-equations with gradient dependent and locally defined reaction
       
Authors: Zhenhai Liu (Yulin Normal Univ., Yulin 537000, China)
         Nikolaos S. Papageorgiou (National Technical Univ., Athens, Greece)

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.

Submitted October 17, 2020. Published April 30, 2021.
Math Subject Classifications: 35J20, 35J60,35J92.
Key Words: (p,q)-differential operator; convection; fixed point; nonlinear;
           regularity; positive solution; Leray-Schauder alternative theorem.