Kanghan Mao, Yiling Zou, Haibo Chen
Abstract:
We study the existence of nontrivial weak solutions for anisotropic \(p\)-Laplacian
systems. A sequence of eigenvalues is characterized through the
\(\mathbb{Z}_2\)-cohomological index on a suitable constraint manifold of Finsler type.
By combining cohomological local splitting with Morse theoretic tools, we prove the
existence of nontrivial solutions to the anisotropic \(p\)-Laplacian system under local
assumptions on the nonlinear terms, both in the nonresonant and resonant cases.
Submitted March 25, 2026. Published July 13, 2026.
Math Subject Classifications: 35P15, 35P30, 35R11.
Key Words: Cohomological local splitting; variational eigenvalues;
existence of solutions; anisotropic p-Laplacian systems.
DOI: 10.58997/ejde.2026.54
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Kanghan Mao School of Mathematics and Statistics Central South University Changsha 410083, China email: maokanghan@163.com |
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Yiling Zou School of Mathematics and Statistics Central South University Changsha 410083, China email: 15074883236@163.com |
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Haibo Chen School of Mathematics and Statistics Central South University Changsha 410083, China email: math_chb@csu.edu.cn |
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