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A critical Kirchhoff‐type problem involving the p & q ‐Laplacian
Author(s) -
Cammaroto F.,
Vilasi L.
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300045
Subject(s) - mathematics , mountain pass , mountain pass theorem , type (biology) , laplace operator , p laplacian , term (time) , mathematical analysis , pure mathematics , nonlinear system , quantum mechanics , physics , boundary value problem , ecology , biology
In this paper we provide an existence result for a nonlocal problem of Kirchhoff‐type which involves both the p ‐ and the q ‐Laplacian and contains a critical term. Our approach is variational: we derive the existence of one non‐trivial solution via the multidimensional mountain pass theorem.