Three solutions for a quasilinear inclusion systems driven by a nonstandard Laplacian operator in ℝN
Abstract
This paper establishes the existence of three distinct weak solutions for a class of nonhomogeneous quasilinear inclusion systems, which are governed by locally Lipschitz functionals within Orlicz-Sobolev spaces over unbounded domains ℝN.By employing a new three critical points theorem established by Wu-Zhou in [29], we extend the nonsmooth critical point theory to handle scenarios with nonlinear growth conditions.Our analysis imposes a precise structural condition on the nonlinear term H, requiring it to exhibit superlinear growth while maintaining subcritical asymptotic behavior. This condition establishes a delicate balance between growth restrictions and functional analytic requirements. The novelties of this work include the construction of suitable energy functionals that are consistent with both the structure of Orlicz-Sobolev spaces and the characteristics of nonlinear growth. Through rigorous variational analysis and careful estimation techniques, we establish the existence of three weak solutions under these generalized conditions, thereby significantly expanding the applicability of critical point methods in nonstandard function spaces.
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BibTeX
@misc{liu2026three,
title = {{Three solutions for a quasilinear inclusion systems driven by a nonstandard Laplacian operator in $\mathbbR^N$}},
author = {Cuiling Liu and Xingyong Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20342},
eprint = {2609.20342},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20342},
}
RIS
TY - UNPB
TI - Three solutions for a quasilinear inclusion systems driven by a nonstandard Laplacian operator in ℝ^N
AU - Cuiling Liu
AU - Xingyong Zhang
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20342
UR - https://arxiv.org/abs/2609.20342
AB - This paper establishes the existence of three distinct weak solutions for a class of nonhomogeneous quasilinear inclusion systems, which are governed by locally Lipschitz functionals within Orlicz-Sobolev spaces over unbounded domains ℝ^N.By employing a new three critical points theorem established by Wu-Zhou in [29], we extend the nonsmooth critical point theory to handle scenarios with nonlinear growth conditions.Our analysis imposes a precise structural condition on the nonlinear term H, requiring it to exhibit superlinear growth while maintaining subcritical asymptotic behavior. This condition establishes a delicate balance between growth restrictions and functional analytic requirements. The novelties of this work include the construction of suitable energy functionals that are consistent with both the structure of Orlicz-Sobolev spaces and the characteristics of nonlinear growth. Through rigorous variational analysis and careful estimation techniques, we establish the existence of three weak solutions under these generalized conditions, thereby significantly expanding the applicability of critical point methods in nonstandard function spaces.
ER -