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Existence and iteration of positive solutions for a singular two-point boundary value problem with a p-Laplacian operator

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Abstract

In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation (ϕ p (u′))′+q(t)f(u) = 0, 0 < t < 1, where ϕ p (s):= |s|p−2 s, p > 1, subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0; 1.

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Authors and Affiliations

  1. Department of Mathematics, North China Electric Power University, Beijing, 102206, P. R. China

    De-Xiang Ma

  2. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, P. R. China

    Wei-Gao Ge

  3. Department of Computer Science, Hainan Normal University, Haikou, Hainan, 571158, P. R. China

    Zhan-Ji Gui

Authors
  1. De-Xiang Ma
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  2. Wei-Gao Ge
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  3. Zhan-Ji Gui
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Ma, DX., Ge, WG. & Gui, ZJ. Existence and iteration of positive solutions for a singular two-point boundary value problem with a p-Laplacian operator. Czech Math J 57, 135–152 (2007). https://doi.org/10.1007/s10587-007-0050-z

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  • DOI: https://doi.org/10.1007/s10587-007-0050-z

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