Positive solutions for resonant (p, q)-equations with concave terms
We consider a parametric (p, q)-equation with competing nonlinearities in the reaction. There is a parametric concave term and a resonant Caratheordory perturbation. The resonance is with respect to the principal eigenvalue and occurs from the right. So the energy functional of the problem is indefinite. Using variational tools and truncation and comparison techniques we show that for all small values of the parameter the problem has at least two positive smooth solutions.
(p, And variational methods, Concave term, Nonlinear regularity theory, Q)-equation, Resonant term, Strong comparison principle
Hu, Shouchuan, and Nikolas S. Papageorgiou. "Positive solutions for resonant (p, q)-equations with concave terms." Communications on Pure & Applied Analysis 17, no. 6 (2018): 2639.
Communications on Pure and Applied Analysis