High perturbations of quasilinear problems with double criticality

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2021-12
Major/Subject
Mcode
Degree programme
Language
en
Pages
21
1875-1895
Series
MATHEMATISCHE ZEITSCHRIFT, Volume 299, issue 3-4
Abstract
This paper is concerned with the qualitative analysis of solutions to the following class of quasilinear problems {-ΔΦu=f(x,u)inΩ,u=0on∂Ω,where ΔΦu=div(φ(x,|∇u|)∇u) and Φ(x,t)=∫0|t|φ(x,s)sds is a generalized N-function. We assume that Ω ⊂ RN is a smooth bounded domain that contains two open regions Ω N, Ω p with Ω ¯ N∩ Ω ¯ p= ∅. The features of this paper are that - Δ Φu behaves like - Δ Nu on Ω N and - Δ pu on Ω p, and that the growth of f: Ω × R→ R is like that of eα|t|NN-1 on Ω N and as |t|p∗-2t on Ω p when |t| is large enough. The main result establishes the existence of solutions in a suitable Musielak–Sobolev space in the case of high perturbations with respect to the values of a positive parameter.
Description
Funding Information: Claudianor O. Alves was partially supported by CNPq/Brazil 304804/2017-7. The work of Vicenţiu D. Rădulescu was supported by a grant of the Romanian Ministry of Education and Research, CNCS-UEFISCDI, Project number PN-III-P4-ID-PCE-2020-0068, within PNCDI III. Vicenţiu D. Rădulescu was also supported by the Slovenian Research Agency program P1-0292. Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
Keywords
Musielak–Sobolev space, Quasilinear problems, Variational methods
Other note
Citation
Alves, C O, Garain, P & Rădulescu, V D 2021, ' High perturbations of quasilinear problems with double criticality ', MATHEMATISCHE ZEITSCHRIFT, vol. 299, no. 3-4, pp. 1875-1895 . https://doi.org/10.1007/s00209-021-02757-z