PreprintarXiv licencearXiv
Bifurcation phenomena in one-phase quasilinear equations with nonstandard growth
Abstract
The bifurcation phenomenon in a singularly perturbed one-phase free boundary problem governed by the g-Laplacian is established under prescribed boundary conditions. This bifurcation is characterized by the existence of a third solution, obtained via the Mountain Pass Lemma, when the boundary data decreases below a suitable threshold. Moreover, we analyze the asymptotic behavior of the associated evolution problem, proving convergence to stable stationary solutions and showing that the Mountain Pass solution is unstable in this dynamical sense.
Related
- Schauder estimates for quasilinear parabolic equations with general Orlicz growth
- Global c1,α regularity and fine behavior at critical points for quasilinear elliptic equations with Orlicz growth and unbounded drift
- Three solutions for a quasilinear inclusion systems driven by a nonstandard Laplacian operator in ℝN
- Absence of critical mass phenomena in one-dimensional critical quasilinear Keller-Segel systems
- Local and global C1,β-regularity for uniformly elliptic quasilinear equations of p-Laplace and Orlicz-Laplace type
BibTeX
@misc{bessa2026bifurcation,
title = {{Bifurcation phenomena in one-phase quasilinear equations with nonstandard growth}},
author = {Junior da Silva Bessa and Alan Pio Sousa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29438},
eprint = {2609.29438},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29438},
}
RIS
TY - UNPB
TI - Bifurcation phenomena in one-phase quasilinear equations with nonstandard growth
AU - Junior da Silva Bessa
AU - Alan Pio Sousa
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.29438
UR - https://arxiv.org/abs/2609.29438
AB - The bifurcation phenomenon in a singularly perturbed one-phase free boundary problem governed by the g-Laplacian is established under prescribed boundary conditions. This bifurcation is characterized by the existence of a third solution, obtained via the Mountain Pass Lemma, when the boundary data decreases below a suitable threshold. Moreover, we analyze the asymptotic behavior of the associated evolution problem, proving convergence to stable stationary solutions and showing that the Mountain Pass solution is unstable in this dynamical sense.
ER -