Bifurcation for a Class of Fourth-Order Stationary Kuramoto-Sivashinsky Equations Under Navier Boundary Condition

Imed Abid; Soumaya Saanouni; Nihed Trabelsi

Bifurcation for a Class of Fourth-Order Stationary Kuramoto-Sivashinsky Equations Under Navier Boundary Condition

Imed Abid * §

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Soumaya Saanouni

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University of Tunis El Manar

Bifurcation for a Class of Fourth-Order Stationary Kuramoto-Sivashinsky Equations Under Navier Boundary Condition

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Abstract

In this paper, we study the bifurcation of semilinear elliptic problem of fourth-order with Navier boundary conditions. We discuss the existence and the uniqueness of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of problems of bifurcation for a class of elliptic problems we also establish the asymptotic behavior of the solution around the bifurcation point.

References

29 Cites in Article

Reference Format

I Abid,M Jleli,N Trabelsi (2008). WEAK SOLUTIONS OF QUASILINEAR BIHARMONIC PROBLEMS WITH POSITIVE, INCREASING AND CONVEX NONLINEARITIES.
N Ahmed,H Harbi (1998). Mathematical analysis of dynamic models of suspension bridges.
Antonio Ambrosetti,Paul Rabinowitz (1973). Dual variational methods in critical point theory and applications.
S Baraket,M Khtaifi,T Ouni (2015). Singular limit solutions for 4-dimensional stationary Kuramoto-Sivashinsky equations with exponential nonlinearity.
S Baraket,M Khtaifi,T Ouni Singular limit for 4-dimensional general stationary q-Kuramoto-Sivashinsky (q-KS) equations with exponential nonlinearity.
H Ben Omrane,S Khenissy (2014). Positivity preserving results for a biharmonic equation under Dirichlet boundary conditions.
H Brezis (1992). Fig. 1: Behavior of the minimal solution, l > 0 Fig. 2.
Haïm Brezis,Thierry Cazenave,Yvan Martel,Arthur Ramiandrisoa (1996). Blow up for $u_t-\Delta u=g(u)$ revisited.
F Corrêa,J Goncalves,Angelo Roncalli (2010). ON A CLASS OF FOURTH ORDER NONLINEAR ELLIPTIC EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS.
Michael Filippakis,Nikolaos Papageorgiou (2006). MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH A DISCONTINUOUS NONLINEARITY.
S Fucik,A Kufner (1980). Unknown Title.
Marius Ghergu,Vicenţiu Rădulescu (2008). Singular Elliptic Problems: Bifurcation and Asymptotic Analysis.
David Gilbarg,Neil Trudinger (2001). Elliptic Partial Differential Equations of Second Order.
L Hörmander (1983). Hörmander, L., The Analysis of Linear Partial Differential Operators III: Pseudo‐Differential Operators. Berlin‐Heidelberg‐New York‐Tokyo, Springer‐Verlag 1985. VIII, 525 S., DM 138,–. ISBN 3‐540‐13828‐5 (Grundlehren der mathematischen Wissenschaften 274).
Hansjörg Kielhöfer (2003). Bifurcation Theory.
Ac,P Lazer,Mckenna (1990). Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis.
Ac,P Lazer,Mckenna (1994). Global bifurcation and a theorem of Tarantello.
Fanghua Lin,Yisong Yang (2007). Nonlinear non-local elliptic equation modelling electrostatic actuation.
Y Martel (1997). Uniqueness of weak solution for nonlinear elliptic problems.
Petru Mironescu,Vicenţiu Rădulescu (1993). The study of a bifurcation problem associated to an asymptotically linear function.
Petru Mironescu,Vicenţiu Rădulescu (1996). The study of a bifurcation problem associated to an asymptotically linear function.
Cv,Pao (2000). On fourth-order elliptic boundary value problems.
John Pelesko,David Bernstein (2003). Modeling MEMS and NEMS.
V Dulescu (2008). Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations.
S,N Trabelsi (2016). Quasilinear equations with source.
Manel Sanchón (2007). Boundedness of the extremal solution of some -Laplacian problems.
Filippo Gazzola,Hans-Christoph Grunau,Guido Sweers (1991). Polyharmonic Boundary Value Problems.
G Tarantella (1992). A note on a semilinear elliptic problem.
J Velin (2008). A CRITERION FOR EXISTENCE OF A POSITIVE SOLUTION OF A NONLINEAR ELLIPTIC SYSTEM.

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Imed Abid, Soumaya Saanouni, Nihed Trabelsi. 2019. "Bifurcation for a Class of Fourth-Order Stationary Kuramoto-Sivashinsky Equations Under Navier Boundary Condition". Global Journal of Science Frontier Research, Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 18 (GJSFR Volume 18 Issue F8).

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GJSFR Volume 18 Issue F8

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

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Classification

GJSFR-F Classification MSC 2010: 35B32

35B65

35B35

35J62

Submission ReceivedNovember 14, 2018
Peer Review Double Blind
Handling Editor
Accepted December 4, 2018
Published December 17, 2018

Version of record

v1.2

Issue date

February 6, 2019

Language

English

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Article Matrices

Total Score: 147

Country: Tunisia

Subject: Global Journal of Science Frontier Research

Authors: Imed Abid, Soumaya Saanouni, Nihed Trabelsi (PhD/Dr. count: 0)

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