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Paper

Anisotropic (p, q)-equations with gradient dependent reaction

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Published 29 June 2021 • © 2021 IOP Publishing Ltd & London Mathematical Society
, , Citation Nikolaos S Papageorgiou et al 2021 Nonlinearity 34 5319 DOI 10.1088/1361-6544/ac0612

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Author e-mails

npapg@math.ntua.gr

radulescu@inf.ucv.ro

dusan.repovs@guest.arnes.si

Author affiliations

1 National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece

2 Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland

3 Department of Mathematics, University of Craiova, 200585 Craiova, Romania

4 Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia

Author notes

5 Author to whom any correspondence should be addressed.

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Dates

  1. Received 10 September 2020
  2. Revised 14 May 2021
  3. Accepted 27 May 2021
  4. Published

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0951-7715/34/8/5319

Abstract

We consider a Dirichlet problem driven by the anisotropic (p, q)-Laplacian and a reaction with gradient dependence (convection). The presence of the gradient in the source term excludes from consideration a variational approach in dealing with the qualitative analysis of this problem with unbalanced growth. Using the frozen variable method and eventually a fixed point theorem, the main result of this paper establishes that the problem has a positive smooth solution.

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10.1088/1361-6544/ac0612