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Multiplicity results for a class of quasilinear equations with exponential critical growth
Author(s) -
Alves Claudianor O.,
Freitas Luciana R.
Publication year - 2018
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.201500371
Subject(s) - mathematics , multiplicity (mathematics) , laplace operator , exponential function , exponential growth , class (philosophy) , pure mathematics , operator (biology) , function (biology) , mathematical analysis , artificial intelligence , computer science , biochemistry , chemistry , repressor , evolutionary biology , biology , transcription factor , gene
In this work, we prove the existence and multiplicity of positive solutions for the following class of quasilinear elliptic equations:− ε N Δ N u + 1 + μ A ( x )u N − 2 u = f ( u )inR N ,u > 0inR N ,where Δ N is the N‐Laplacian operator, N ≥ 2 , f is a function with exponential critical growth, μ and ε are positive parameters and A is a nonnegative continuous function verifying some hypotheses. To obtain our results, we combine variational arguments and Lusternik–Schnirelman category theory.