Bulletin of the Belgian Mathematical Society - Simon Stevin

Nonlinear Neumann problems with asymmetric nonsmooth potential

Shouchuan Hu and Nikolaos S. Papageorgiou

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Abstract

In this paper we study a scalar Neumann problem driven by the ordinary p-Lapacian and a nonsmooth potential. The nonlinearity exhibits an asymmetric behavior. Namely growth restriction is imposed in one direction only (either the positive direction or the negative direction). Using a variational approach based on the nonsmooth critical point theory for locally Lipschitz function, we prove the existence of a solution.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 3 (2005), 417-433.

Dates
First available in Project Euclid: 8 September 2005

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1126195346

Digital Object Identifier
doi:10.36045/bbms/1126195346

Mathematical Reviews number (MathSciNet)
MR2173704

Zentralblatt MATH identifier
1112.34014

Subjects
Primary: 34B15: Nonlinear boundary value problems

Keywords
p-Laplacian locally function generalized subdifferential nonsmooth critical point theory linking sets asymmetric nonlinearity

Citation

Hu, Shouchuan; Papageorgiou, Nikolaos S. Nonlinear Neumann problems with asymmetric nonsmooth potential. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 3, 417--433. doi:10.36045/bbms/1126195346. https://projecteuclid.org/euclid.bbms/1126195346


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