Embedding theorems for weighted Sobolev spaces in a borderline case and applications

We establish some embedding results for weighted Sobolev spaces. As an application, we obtain one nonzero solution for the equation - div ( | ∇ u | N - 2 ∇ u ) + V ( x ) | u | N - 2 u = λ Q ( x ) f ( u ) , in R N , where V , Q are nonnegative potentials, λ > 0 is a large parameter and f has criti...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2024-02, Vol.203 (1), p.345-359
Main Authors: Carvalho, J. L., Furtado, M. F., Medeiros, E. S.
Format: Article
Language:English
Subjects:
Embedding
Mathematics
Mathematics and Statistics
Sobolev space
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Summary:We establish some embedding results for weighted Sobolev spaces. As an application, we obtain one nonzero solution for the equation - div ( | ∇ u | N - 2 ∇ u ) + V ( x ) | u | N - 2 u = λ Q ( x ) f ( u ) , in R N , where V , Q are nonnegative potentials, λ > 0 is a large parameter and f has critical growth in the Trudinger–Moser sense.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-023-01366-3