Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Elliptic equations and systems with critical Trudinger-Moser nonlinearities

Pages: 455 - 476, Volume 30, Issue 2, June 2011      doi:10.3934/dcds.2011.30.455

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Djairo G. De Figueiredo - IMECC-UNICAMP, Caixa Postal 6065, CEP: 13081-970, Campinas - SP, Brazil (email)
João Marcos do Ó - Departamento de Matemática–Universidade Federal da Paraíba, 58051-900, João Pessoa–PB, Brazil (email)
Bernhard Ruf - Dip. di Matematica, Universita degli Studi, Via Saldini 50, 20133 Milano, Italy (email)

Abstract: In this article we give first a survey on recent results on some Trudinger-Moser type inequalities, and their importance in the study of nonlinear elliptic equations with nonlinearities which have critical growth in the sense of Trudinger-Moser. Furthermore, recent results concerning systems of such equations will be discussed.

Keywords:  Trudinger-Moser inequality, variational methods, critical growth.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: April 2010;      Available Online: February 2011.