Existence of Solutions for a Class of Third Order Quasilinear Ordinary Differential Equations with Nonlinear Boundary Value Problems

نویسندگان

  • Jianqing Zhao
  • Zuodong Yang
  • Meng Fan
  • Z. Yang
چکیده

In this paper, we are concerned with the third-order quasilinear ordinary differential equation (Φp(u)) = f(t, u, u′, u′′), 0 < t < 1, with the nonlinear boundary conditions u(0) = 0, g(u′(0), u′′(0)) = A, h(u′(1), u′′(1)) = B or u(0) = C, L(u′(0), u′(1)) = 0, R(u′(0), u′(1), u′′(0), u′′(1)) = 0, where A,B, C ∈ R,Φp(u) = |u|p−2u(p > 1), f : [0, 1]× R → R is continuous, g, h, L : R → R, R : R → R are continuous, which occurs in the study of the p-Laplace equation, generalized reaction-diffusion theory, non-Newtonian fluid theory, and the turbulent flow of a gas in porous medium. Existence results are obtained by using a Nagumo condition and upper and lower solutions methods. AMS Subject Classifications: 34B40.

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تاریخ انتشار 2009