Masmoudi, SyrineZribi, Malek2020-09-142020-09-142003-02-28Masmoudi, S., & Zribi, M. (2003). Nonlinear singular Navier problem of fourth order. <i>Electronic Journal of Differential Equations, 2003</i>(19), pp. 1-12.1072-6691https://hdl.handle.net/10877/12610We present an existence result for a nonlinear singular differential equation of fourth order with Navier boundary conditions. Under appropriate conditions on the nonlinearity ƒ(t, x, y), we prove that the problem L2u = L(Lu) = ƒ(., u, Lu) a.e. in (0, 1), u'(0) = 0, (Lu)' (0) = 0, u(1) = 0, Lu(1) = 0. has a positive solution behaving like (1 - t) on [0, 1]. Here L is a differential operator of second order, Lu = 1/A(au')'. For f(t, x, y) = f(t, x), we prove a uniqueness result. Our approach is based on estimates for Green functions and on Schauder's fixed point theorem.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear singular Navier problemGreen functionPositive solutionArticle