Electron. J. Differential Equations, Vol. 2025 (2025), No. 06, pp. 1-14.
Weighted (p,q)-equations with gradient dependent reaction
Zhao Jing, Zhenhai Liu, Nikolaos S. Papageorgiou
Abstract:
We consider a weighted (p,q)-equation with a parametric reaction
depending on the gradient. Using truncation and comparison techniques
and the theory of nonlinear operators of monotone type, we show
that for all small values of the parameter, the problem has a
positive smooth solution.
Submitted February 25, 2024. Published January 13, 2025.
Math Subject Classifications: 35J60, 35J91.
Key Words: Weighted (p,q)-operator; principal eigenvalue; truncation; pseudo-monotone map; gradient dependence.
DOI: 10.58997/ejde.2025.06
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Zhao Jing
School of Mathematics and Quantitative economics
Guangxi University of Finance and Economics
Nanning, Guangxi 530003, China
email: jingzhao100@126.com
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Zhenhai Liu
Guangxi Colleges and Universities Key Laboratory
of Optimization Control and Engineering Calculation
Guangxi Minzu University, Nanning, Guangxi, 530006, China
email: zhhliu@hotmail.com
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Nikolaos S. Papageorgiou
Department of Mathematics,
National Technical University
Zografou Campus, 15780 Athens, Greece
email: npapg@math.ntua.gr
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