Liu, ZhenhaiPapageorgiou, Nikolaos S.2021-08-232021-08-232021-04-30Liu, Z., & Papageorgiou, N. S. (2021). Dirichlet (p,q)-equations with gradient dependent and locally defined reaction. <i>Electronic Journal of Differential Equations, 2021</i>(34), pp. 1-8.1072-6691https://hdl.handle.net/10877/14431We 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.Text8 pages1 file (.pdf)enAttribution 4.0 International(p,q)-differential operatorConvectionFixed pointNonlinearRegularityPositive solutionLeray-Schauder alternative theoremArticle