Constant sign and nodal solutions for resonant double phase problems

Nikolaos S. Papageorgiou; Vicenţiu D. Rădulescu; Yitian Wang

doi:10.54330/afm.141250

Kirjoittajat

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

Avainsanat:

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

Abstrakti

We consider a double phase Dirichlet problem with a reaction which asymptotically as

x \to \pm \infty

can be resonant with respect to the principle eigenvalue

{\hat{λ}}_{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).

Constant sign and nodal solutions for resonant double phase problems

Kirjoittajat

Avainsanat:

Abstrakti

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