Bifurcation for a Class of Fourth-Order Stationary Kuramoto-Sivashinsky Equations Under Navier Boundary Condition
bifurcation, regularity, stability, quasilinear
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.
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I Abid, M Jleli, N Trabelsi (2008) WEAK SOLUTIONS OF QUASILINEAR BIHARMONIC PROBLEMS WITH POSITIVE, INCREASING AND CONVEX NONLINEARITIES. 06(03), 213-227.
N Ahmed, H Harbi (1998) Mathematical analysis of dynamic models of suspension bridges. 58, 853-874.
Antonio Ambrosetti, Paul Rabinowitz (1973) Dual variational methods in critical point theory and applications. 14(4), 349-381.
S Baraket, M Khtaifi, T Ouni (2015) Singular limit solutions for 4-dimensional stationary Kuramoto-Sivashinsky equations with exponential nonlinearity. 2015(187), 1-26.
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. 34(3), 601-608.
H Brezis (1992) Fig. 1: Behavior of the minimal solution, l > 0 Fig. 2. 0.
Haïm Brezis, Thierry Cazenave, Yvan Martel, Arthur Ramiandrisoa (1996) Blow up for $u_t-Delta u=g(u)$ revisited. 1(1), 73-90.
F Corrêa, J Goncalves, Angelo Roncalli (2010) ON A CLASS OF FOURTH ORDER NONLINEAR ELLIPTIC EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS. 08(02), 185-197.
Michael Filippakis, Nikolaos Papageorgiou (2006) MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH A DISCONTINUOUS NONLINEARITY. 04(01), 1-18.
S Fucik, A Kufner (1980) Unknown Title. 2.
Marius Ghergu, Vicenţiu Rădulescu (2008) Singular Elliptic Problems: Bifurcation and Asymptotic Analysis. 37.
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). 67(11), 579-579.
Hansjörg Kielhöfer (2003) Bifurcation Theory.
Ac, P Lazer, Mckenna (1990) Large-amplitude periodic oscillations in suspension bridges: some new connections with nonlinear analysis. 32(4), 537-578.
Ac, P Lazer, Mckenna (1994) Global bifurcation and a theorem of Tarantello. 181(3), 648-655.
Fanghua Lin, Yisong Yang (2007) Nonlinear non-local elliptic equation modelling electrostatic actuation. 463(2081), 1323-1337.
Y Martel (1997) Uniqueness of weak solution for nonlinear elliptic problems. 23, 161-168.
Petru Mironescu, Vicenţiu Rădulescu (1993) The study of a bifurcation problem associated to an asymptotically linear function. 26(4), 857-875.
Petru Mironescu, Vicenţiu Rădulescu (1996) The study of a bifurcation problem associated to an asymptotically linear function. 26(4), 857-875.
Cv, Pao (2000) On fourth-order elliptic boundary value problems. 128, 1023-1030.
John Pelesko, David Bernstein (2003) Modeling MEMS and NEMS.
V Dulescu (2008) Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations. 6.
S, N Trabelsi (2016) Quasilinear equations with source. 2016, 367-442.
Manel Sanchón (2007) Boundedness of the extremal solution of some -Laplacian problems. 67(1), 281-294.
Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers (1991) Polyharmonic Boundary Value Problems.
G Tarantella (1992) A note on a semilinear elliptic problem. 5(3), 561-565.
J Velin (2008) A CRITERION FOR EXISTENCE OF A POSITIVE SOLUTION OF A NONLINEAR ELLIPTIC SYSTEM. 06(03), 299-321.
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2019-02-06
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