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Positive Solutions for Resonant (p, q)-equations with convection

Authors
  • Liu, Zhenhai1, 2
  • Papageorgiou, Nikolaos S.3
  • 1 Yulin Normal University, 537000 , (China)
  • 2 Guangxi University for Nationalities, Nanning, 530006 , (China)
  • 3 National Technical University, Zografou Campus, 15780 , (Greece)
Type
Published Article
Journal
Advances in Nonlinear Analysis
Publisher
De Gruyter
Publication Date
Jul 17, 2020
Volume
10
Issue
1
Pages
217–232
Identifiers
DOI: 10.1515/anona-2020-0108
Source
De Gruyter
Keywords
License
Green

Abstract

We consider a nonlinear parametric Dirichlet problem driven by the (p, q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. A parametric one consisting of the sum of a singular term and of a drift term (convection) and of a nonparametric perturbation which is resonant. Using the frozen variable method and eventually a fixed point argument based on an iterative asymptotic process, we show that the problem has a positive smooth solution.

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