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 |
| Nikolaos S. Papageorgiou Department of Mathematics, National Technical University Zografou Campus, 15780 Athens, Greece email: npapg@math.ntua.gr |
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