Acta mathematica scientia, Series B >
A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION
Received date: 2015-05-27
Revised date: 2016-04-25
Online published: 2016-12-25
We study the existence of positive solutions to a two-order semilinear elliptic problem with Dirichlet boundary condition
(Pλ) 
-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.
Key words： extremal solution; regularity; bifurcation; stability
Soumaya SÂ , ANOUNI , Nihed TRABELSI . A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION[J]. Acta mathematica scientia, Series B, 2016 , 36(6) : 1731 -1746 . DOI: 10.1016/S0252-9602(16)30102-3
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