Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 06, pp. 1-14.

Title: Weighted (p,q)-equations with gradient dependent reaction

Authors: Zhao Jing (Guangxi Univ. of Finance and Economics, Nanning, Guangxi, China)
         Zhenhai Liu (Guangxi Minzu Univ., Nanning, Guangxi, China)
         Nikolaos S. Papageorgiou (National Technical Univ., Zografou, Athens, Greece)
  
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.