# American Institute of Mathematical Sciences

November  2018, 17(6): 2639-2656. doi: 10.3934/cpaa.2018125

## Positive solutions for resonant (p, q)-equations with concave terms

 1 College of Mathematics, Shandong Normal University, Jinan, Shandong, China 2 Department of Mathematics, Missouri State University, Springfield, MO 65804, USA 3 Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

Received  November 2017 Revised  April 2018 Published  June 2018

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.

Citation: Shouchuan Hu, Nikolas S. Papageorgiou. Positive solutions for resonant (p, q)-equations with concave terms. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2639-2656. doi: 10.3934/cpaa.2018125
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