Geodesic
Constant sign and nodal solutions for resonant double phase problems
Nikolaos S. Papageorgiou1 ; Vicenţiu D. Rădulescu2 ; Yitian Wang3
1 National Technical University, Department of Mathematics, and University of Craiova, Department of Mathematics
2 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
3 Harbin Engineering University, College of Mathematical Sciences, and University of Craiova, Department of Mathematics
Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 757-777.

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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).
DOI : 10.54330/afm.141250
Keywords: Double phase operator, unbalanced growth, generalized Orlicz spaces, resonant equation, multiple solutions with sign information

Nikolaos S. Papageorgiou 1 ; Vicenţiu D. Rădulescu 2 ; Yitian Wang 3

1 National Technical University, Department of Mathematics, and University of Craiova, Department of Mathematics
2 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
3 Harbin Engineering University, College of Mathematical Sciences, and University of Craiova, Department of Mathematics 
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Nikolaos S. Papageorgiou; Vicenţiu D. Rădulescu; Yitian Wang. Constant sign and nodal solutions for resonant double phase problems. Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 757-777. doi : 10.54330/afm.141250. http://geodesic.mathdoc.fr/articles/10.54330/afm.141250/

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