(N,q)‐Laplacian problems with critical Trudinger‐Moser nonlinearities
By Yang Yang, Kanishka Perera. 2014
48 citations recorded by the source corpus.
We obtain nontrivial solutions of an (N,q) ‐Laplacian problem with a critical Trudinger–Moser nonlinearity in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical nonlinearities, this problem lacks a direct sum decomposition suitable for applying the classical linking theorem. We show that every Palais–Smale sequence at a level below a certain energy threshold admits a subsequence that converges weakly to a nontrivial critical point of the variational functional. Then we prove an abstract critical point theorem based on a cohomological index and use it to construct a minimax level below this threshold.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/cd75f065694f881c11f1c57c10831db1c78b625a
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In Applied Mathematics
- Marco Squassina
- Yang Yang
- Sunra Mosconi
- Kanishka Perera
- Julián Fernández Bonder
- Analía Silva
- Nicolas Saintier
- Patrick Winkert
In Computational Theory and Mathematics
- Marco Squassina
- Yang Yang
- Sunra Mosconi
- Kanishka Perera
- Analía Silva
- Julián Fernández Bonder
- Nicolas Saintier
- Patrick Winkert
Citations in the corpus
- The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem (2018, methodology): “In fact, following the ideas of [30], one applies a Linking theorem due to Yang and Perera in [43] (see also [10]) exactly in the same way as in [30] with the obvious modifications.”
- The Brezis–Nirenberg problem for the fractional p-Laplacian (2015, methodology): “n [4]. The second difficulty is the lack of a direct sum decomposition suitable for applying the classical linking theorem. We use an abstract linking theorem based on the cohomological index proved in [48] to overcome this difficulty. Contents 1. Introduction and main result 1 Acknowledgments 5 2. Prel”