A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION

doi:10.1016/S0252-9602(16)30102-3

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (6): 1731-1746.doi: 10.1016/S0252-9602(16)30102-3

A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION

Soumaya SÂANOUNI¹, Nihed TRABELSI²

1. Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, Campus University 2092 Tunis, Tunisia;
2. Higher Institut of Medicals Technologies of Tunis, University of Tunis El Manar, 9 Street Dr. Zouhair Essafi 1006 Tunis, Tunisia

收稿日期:2015-05-27 修回日期:2016-04-25 出版日期:2016-12-25 发布日期:2016-12-25
作者简介:Soumaya SÂANOUNI,E-mail:saanouni.soumaya@yahoo.com;Nihed TRABELSI,E-mail:nihed.trabelsi78@gmail.com

A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION

Soumaya SÂANOUNI¹, Nihed TRABELSI²

1. Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, Campus University 2092 Tunis, Tunisia;
2. Higher Institut of Medicals Technologies of Tunis, University of Tunis El Manar, 9 Street Dr. Zouhair Essafi 1006 Tunis, Tunisia

Received:2015-05-27 Revised:2016-04-25 Online:2016-12-25 Published:2016-12-25

摘要/Abstract

摘要：

We study the existence of positive solutions to a two-order semilinear elliptic problem with Dirichlet boundary condition
(P_λ) -div(c(x)∇u)=λf(u) in Ω,
u=0 on ∂Ω,
where Ω⊂Rⁿ; n≥2 is a smooth bounded domain; f is a positive, increasing and convex source term and c(x) is a smooth bounded positive function on Ω. We also prove the existence of critical value and claim the uniqueness of extremal solutions.

关键词: extremal solution, regularity, bifurcation, stability

Abstract:

Key words: extremal solution, regularity, bifurcation, stability

中图分类号:

35B65

Soumaya SÂANOUNI, Nihed TRABELSI. A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION[J]. 数学物理学报(英文版), 2016, 36(6): 1731-1746.

Soumaya SÂANOUNI, Nihed TRABELSI. A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION[J]. Acta mathematica scientia,Series B, 2016, 36(6): 1731-1746.

参考文献

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A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION

A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION

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