Constant sign and nodal solutions for resonant double phase problems

Författare

  • 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

Nyckelord:

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).

Nedladdningar

Publicerad

2023-11-21

Nummer

Vol 48 Nr 2 (2023)

Sektion

Articles

Licens

Copyright (c) 2023 Annales Fennici Mathematici

Creative Commons-licens

Detta verk är licensierat under en Creative Commons Erkännande-IckeKommersiell 4.0 Internationell-licens.

Referera så här

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