Bulletin of the Belgian Mathematical Society - Simon Stevin

Multiplicity of solutions for anisotropic quasilinear elliptic equations with variable exponents

Denisa Stancu-Dumitru

Full-text: Open access

Abstract

We study an anisotropic partial differential equation on a bounded domain $\Omega\subset\mathbb R^N$. We prove the existence of at least two nontrivial weak solutions using as main tools the mountain pass lemma and Ekeland's variational principle.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 5 (2010), 875-889.

Dates
First available in Project Euclid: 14 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1292334062

Digital Object Identifier
doi:10.36045/bbms/1292334062

Mathematical Reviews number (MathSciNet)
MR2777777

Zentralblatt MATH identifier
1205.35126

Subjects
Primary: 35D05 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 68T40: Robotics [See also 93C85] 76A02: Foundations of fluid mechanics

Keywords
anisotropic equation variable exponent weak solution mountain-pass theorem Ekeland's variational principle

Citation

Stancu-Dumitru, Denisa. Multiplicity of solutions for anisotropic quasilinear elliptic equations with variable exponents. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 5, 875--889. doi:10.36045/bbms/1292334062. https://projecteuclid.org/euclid.bbms/1292334062


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