Ground states for Brezis-Nirenberg-type fractional elliptic systems with sublinear absorption and subcritical perturbation
Abstract
This paper addresses the non-local fractional counterpart of the Laplace equation involving critical nonlinearities, a famous problem originally investigated by Brezis and Nirenberg in [Comm. Pure Appl. Math. 36(4) (1983), pp. 437--477]. We study a class of fractional elliptic systems and equations with critical exponents, sublinear absorption, subcritical perturbation, and general noncoercive frequency parameters. The work is carried out both within a general framework involving non-local integrodifferential operators and in specific concrete models. Our results extend and complement the existing literature on critical fractional elliptic problems in several directions: (1) we include sublinear absorption together with a subcritical perturbation, so that the overall nonlinearity is not superlinear at zero; (2) we provide two types of concrete verification of the energy threshold condition in the presence of the critical term, the sublinear absorption, and the subcritical perturbation, whereas the existing verifications are restricted to the pure critical case; (3) we obtain ground state solutions for coupled systems, not merely nontrivial solutions for scalar equations; (4) we allow a general noncoercive range of frequency parameters, including negative values.
Related
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- Classification of radially symmetric solutions to a Hardy-Hénon equation with sublinear absorption and applications
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- A Quantitative Gidas--Ni--Nirenberg Theorem for the Fractional Laplacian
- Fractional and anisotropic Gagliardo--Nirenberg inequalities with applications
BibTeX
@misc{chen2026ground,
title = {{Ground states for Brezis-Nirenberg-type fractional elliptic systems with sublinear absorption and subcritical perturbation}},
author = {Guanwei Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35365},
eprint = {2610.35365},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35365},
}
RIS
TY - UNPB
TI - Ground states for Brezis-Nirenberg-type fractional elliptic systems with sublinear absorption and subcritical perturbation
AU - Guanwei Chen
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35365
UR - https://arxiv.org/abs/2610.35365
AB - This paper addresses the non-local fractional counterpart of the Laplace equation involving critical nonlinearities, a famous problem originally investigated by Brezis and Nirenberg in [Comm. Pure Appl. Math. 36(4) (1983), pp. 437--477]. We study a class of fractional elliptic systems and equations with critical exponents, sublinear absorption, subcritical perturbation, and general noncoercive frequency parameters. The work is carried out both within a general framework involving non-local integrodifferential operators and in specific concrete models. Our results extend and complement the existing literature on critical fractional elliptic problems in several directions: (1) we include sublinear absorption together with a subcritical perturbation, so that the overall nonlinearity is not superlinear at zero; (2) we provide two types of concrete verification of the energy threshold condition in the presence of the critical term, the sublinear absorption, and the subcritical perturbation, whereas the existing verifications are restricted to the pure critical case; (3) we obtain ground state solutions for coupled systems, not merely nontrivial solutions for scalar equations; (4) we allow a general noncoercive range of frequency parameters, including negative values.
ER -