Saanouni, SoumayaTrabelsi, Nihed2023-06-202023-06-202016-04-06Sâanouni, S., & Trabelsi, N. (2016). Bifurcation for elliptic forth-order problems with quasilinear source term. <i>Electronic Journal of Differential Equations, 2016</i>(92), pp. 1-16.1072-6691https://hdl.handle.net/10877/16964We 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.Text16 pages1 file (.pdf)enAttribution 4.0 InternationalbifurcationregularitystabilityquasilinearArticle