Constant sign and nodal solutions for resonant double phase problems

Authors

  • Nikolaos S. Papageorgiou National Technical University, Department of Mathematics, and University of Craiova, Department of Mathematics
  • Vicenţiu D. Rădulescu AGH University of Kraków, Faculty of Applied Mathematics, and Brno University of Technology, Faculty of Electrical Engineering and Communication, and University of Craiova, Department of Mathematics, and Simion Stoilow Institute of Mathematics of the Romanian Academy, and Zhejiang Normal University, School of Mathematics
  • Yitian Wang Harbin Engineering University, College of Mathematical Sciences, and University of Craiova, Department of Mathematics

DOI:

https://doi.org/10.54330/afm.141250

Keywords:

Double phase operator, unbalanced growth, generalized Orlicz spaces, resonant equation, multiple solutions with sign information

Abstract

We consider a double phase Dirichlet problem with a reaction which asymptotically as \(x \rightarrow \pm \infty\) can be resonant with respect to the principle eigenvalue \(\hat{\lambda}_{1}>0\) of the Dirichlet weighted \(p\)-Laplacian. Using variational tools, together with truncation and comparison techniques and critical groups, we show that the problem has at least three bounded solutions which are ordered and we provide sign information for all of them (positive, negative and nodal).

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Published

2023-11-21

Issue

Vol. 48 No. 2 (2023)

Section

Articles

License

Copyright (c) 2023 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Papageorgiou, N. S., Rădulescu, V. D., & Wang, Y. (2023). Constant sign and nodal solutions for resonant double phase problems. Annales Fennici Mathematici, 48(2), 757-777. https://doi.org/10.54330/afm.141250