Zuodong Yang

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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(More)
We consider the boundary blow-up nonlinear elliptic problems ∆u ± λ|∇u|q = k(x)g(u) in a bounded domain with boundary condition u|∂Ω = +∞, where q ∈ [0, 2] and λ ≥ 0. Under suitable growth assumptions on k near the boundary and on g both at zero and at infinity, we show the existence of at least one solution in C2(Ω). Our proof is based on the method of(More)
This paper deals with nonlinear degenerate parabolic (porous medium) system with localized sources. It is shown that under certain conditions solutions of the equation blow up in finite time for large a and b or large initial data while there exist global positive solutions for small a and b or small initial data. Moreover, it is also shown that all global(More)
In this paper, our main purpose is to consider the quasilinear equation 0096-3 doi:10. q Pro Educa 2003SX E-m divðjruj ruÞ 1⁄4 mðxÞf ðuÞ on a domain X R, N P 3, where f is a nonnegative, nondecreasing continuous function which vanishes at the origin, and m is a nonnegative continuous function with the property that any zero of m is contained in a bounded(More)