Bifurcation for elliptic forth-order problems with quasilinear source term
Date
2016-04-06
Authors
Saanouni, Soumaya
Trabelsi, Nihed
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study the bifurcations of the semilinear elliptic forth-order problem with Navier boundary conditions
∆2u - div(c(x)∇u) = λƒ(u) in Ω,
∆u = u = 0 on ∂Ω.
Where Ω ⊂ ℝn, n ≥ 2 is a smooth bounded domain, ƒ is a positive, increasing and convex source term and c(x) is a smooth positive function on Ω̅ such that the L∞-norm of its gradient is small enough. We prove the existence, uniqueness and stability of positive solutions. We also show the existence of critical value λ* and the uniqueness of its extremal solutions.
Description
Keywords
bifurcation, regularity, stability, quasilinear
Citation
Sâanouni, S., & Trabelsi, N. (2016). Bifurcation for elliptic forth-order problems with quasilinear source term. <i>Electronic Journal of Differential Equations, 2016</i>(92), pp. 1-16.
Rights
Attribution 4.0 International