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Advances in Nonlinear Analysis

Editor-in-Chief: Radulescu, Vicentiu / Squassina, Marco

IMPACT FACTOR 2018: 6.636

CiteScore 2018: 5.03

SCImago Journal Rank (SJR) 2018: 3.215
Source Normalized Impact per Paper (SNIP) 2018: 3.225

Mathematical Citation Quotient (MCQ) 2017: 1.89

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Some remarks for one-dimensional mean curvature problems through a local minimization principle

Ghasem A. Afrouzi / Armin Hadjian / Giovanni Molica Bisci
  • Dipartimento P.A.U., Università degli Studi “Mediterranea” di Reggio Calabria, Salita Melissari – Feo di Vito, 89100 Reggio Calabria, Italy
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Published Online: 2013-10-16 | DOI: https://doi.org/10.1515/anona-2013-0021


In this paper we deal with a bifurcation result for the following parametric one-dimensional mean curvature problem:

where and is a Carathéodory function vanishing at zero. More precisely, a critical point theorem (local minimum result) for differentiable functionals is exploited in order to prove that the above problem admits at least one nontrivial and nonnegative weak solution under an asymptotical behaviour of the nonlinear datum at zero. A concrete example of an application is then presented.

Keywords: One-dimensional prescribed curvature problem; variational methods; existence results

About the article

Received: 2013-09-25

Revised: 2013-09-30

Accepted: 2013-09-30

Published Online: 2013-10-16

Published in Print: 2013-11-01

Citation Information: Advances in Nonlinear Analysis, Volume 2, Issue 4, Pages 427–441, ISSN (Online) 2191-950X, ISSN (Print) 2191-9496, DOI: https://doi.org/10.1515/anona-2013-0021.

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