Bulletin of the Belgian Mathematical Society - Simon Stevin

On some quasilinear elliptic equations with critical Sobolev exponents and non-standard growth conditions

Lucia Calotă

Full-text: Open access

Abstract

In this paper we study a class of quasilinear elliptic problems involving critical exponents and non-standard growth condition. We establish the existence of at least one nontrivial solution using as main tool Ekeland's variational principle.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 2 (2008), 249-256.

Dates
First available in Project Euclid: 8 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1210254822

Digital Object Identifier
doi:10.36045/bbms/1210254822

Mathematical Reviews number (MathSciNet)
MR2424110

Zentralblatt MATH identifier
1157.35039

Subjects
Primary: 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 35J65: Nonlinear boundary value problems for linear elliptic equations

Keywords
quasilinear elliptic equation weak solution critical Sobolev exponent variable exponent Lebesgue space

Citation

Calotă, Lucia. On some quasilinear elliptic equations with critical Sobolev exponents and non-standard growth conditions. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 2, 249--256. doi:10.36045/bbms/1210254822. https://projecteuclid.org/euclid.bbms/1210254822


Export citation