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Quasilinear elliptic equations with slowly growing principal part and critical Orlicz–Sobolev nonlinear term

Published online by Cambridge University Press:  13 March 2009

Nobuyoshi Fukagai ,
Masayuki Ito  and
Kimiaki Narukawa
Nobuyoshi Fukagai
Affiliation:
Department of Mathematics, Faculty of Engineering, Tokushima University, Tokushima 770-8506, Japan (fukagai@pm.tokushima-u.ac.jp)
Masayuki Ito
Affiliation:
Department of Mathematics and Computer Sciences, Tokushima University, Tokushima 770-8502, Japan (mas-ito@ias.tokushima-u.ac.jp)
Kimiaki Narukawa
Affiliation:
Department of Mathematics, Naruto University of Education, Takashima, Naruto 772-8502, Japan (knaru@naruto.ac.jp)
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Abstract

A variational problem for a functional with slowly growing principal part and involving critical Orlicz–Sobolev lower term with respect to the principal part is discussed. The principal part of the functional is not Fréchet differentiable. The lack of differentiability and the critical growth rate of the lower term demand a precise compactness argument in the variational approach. A non-negative solution for the Euler equation is given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 1 , February 2009 , pp. 73 - 106
Copyright
Copyright © Royal Society of Edinburgh 2009

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