Electron. J. Differential Equations, Vol. 2021 (2021), No. 34, pp. 1-8.

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

Zhenhai Liu, Nikolaos S. Papageorgiou

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.

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Zhenhai Liu
Guangxi Colleges and Universities Key Laboratory of
Complex System Optimization and Big Data Processing
Yulin Normal University
Yulin 537000, China
email: zhhliu@hotmail.com
  Nikolaos S. Papageorgiou
Department of Mathematics
National Technical University
Zografou Campus, 15780 Athens, Greece
email: npapg@math.ntua.gr

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