Nonlinear singular Navier problem of fourth order
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We 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.
CitationMasmoudi, S., & Zribi, M. (2003). Nonlinear singular Navier problem of fourth order. Electronic Journal of Differential Equations, 2003(19), pp. 1-12.
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