Open AccessBifurcation analysis for degenerate problems with mixed regime and absorption
Author(s) -
Ahmed Alsaedi,
Vicenţiu D. Rădulescu,
Bashir Ahmad
Publication year - 2020
Publication title -
bulletin of mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.407
H-Index - 21
eISSN - 1664-3607
pISSN - 1664-3615
DOI - 10.1142/s1664360720500174
Subject(s) - degenerate energy levels , transonic , bifurcation , operator (biology) , absorption (acoustics) , mathematics , type (biology) , mathematical analysis , flow (mathematics) , nonlinear system , physics , chemistry , mechanics , geometry , quantum mechanics , geology , biochemistry , repressor , transcription factor , aerodynamics , gene , paleontology , acoustics
We are concerned with the study of a bifurcation problem driven by a degenerate operator of Baouendi–Grushin type. Due to its degenerate structure, this differential operator has a mixed regime. Studying the combined effects generated by the absorption and the reaction terms, we establish the bifurcation behavior in two cases. First, if the absorption nonlinearity is dominating, then the problem admits solutions only for high perturbations of the reaction. In the case when the reaction dominates the absorption term, we prove that the problem admits nontrivial solutions for all the values of the parameter. The analysis developed in this paper is associated with patterns describing transonic flow restricted to subsonic regions.