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

Shouchuan Hu; Nikolas S. Papageorgiou

doi:10.3934/cpaa.2018125

Article Contents

2018, Volume 17, Issue 6: 2639-2656. Doi: 10.3934/cpaa.2018125

This issue Previous Article Ground states for Kirchhoff-type equations with critical growth Next Article Local well-posedness for the Zakharov system on the background of a line soliton

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

Shouchuan Hu^1,2, and
Nikolas S. Papageorgiou^3,

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: October 31, 2017

Revised: March 31, 2018

Published: June 2018

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Abstract

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.

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Mathematics Subject Classification: 35J20, 35J92.

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References

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