Constant Sign and Nodal Solutions for Variable Exponent Double Phase Problem
In this work, we investigate the existence of at least three solutions to a variable exponent double-phase problem with a reaction term that is only locally Lipschitz continuous. Additionally, we analyse the sign properties of these solutions. Specifically, we establish the existence of two constant-sign solutions, one positive and one negative, using the Mountain Pass Theorem. The third solution, which is nodal (i.e., it changes sign), is obtained via the Nehari manifold approach. Finally, we demonstrate that the nodal solution has exactly two nodal domains.
Authors
- Leszek Gasiński (ORCID: https://orcid.org/0000-0001-8692-6442)
- Νικόλαος Παπαγεωργίου (ORCID: https://orcid.org/0000-0002-2063-2510)
- Giuseppe Failla (ORCID: https://orcid.org/0009-0007-7336-4410)
Institutions
- University of Messina (IT)
- Uniwersytet Komisji Edukacji Narodowej w Krakowie (PL)
- National Technical University of Athens (GR)
Publication Details
- Journal
- Results in Mathematics
- Published
- 2025-06-27
- DOI
- https://doi.org/10.1007/s00025-025-02449-8
- Citations
- 1
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 3.73
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni