A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION

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

Abstract

Abstract:

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.

Key words: extremal solution, regularity, bifurcation, stability

CLC Number:

35B65

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

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