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On a class of critical N-Laplacian problems

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  27 June 2022

Tsz Chung Ho  and
Kanishka Perera
Tsz Chung Ho
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA (tho2011@my.fit.edu; kperera@fit.edu)
Kanishka Perera
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA (tho2011@my.fit.edu; kperera@fit.edu)
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Abstract

We establish some existence results for a class of critical $N$-Laplacian problems in a bounded domain in $\mathbb {R}^{N}$. In the absence of a suitable direct sum decomposition of the underlying Sobolev space to which the classical linking theorem can be applied, we use an abstract linking theorem based on the $\mathbb {Z}_2$-cohomological index to obtain a non-trivial critical point.

Keywords

critical N-Laplacian problemsexistencecritical pointslinkingℤ2-cohomological index

MSC classification

Primary: 35J92: Quasilinear elliptic equations with $p$-Laplacian
Secondary: 35B33: Critical exponents 35B38: Critical points
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 2 , May 2022 , pp. 556 - 576
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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