1 results
On a class of critical N-Laplacian problems
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 2 / May 2022
- Published online by Cambridge University Press:
- 27 June 2022, pp. 556-576
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- Article
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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.
