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Existence and iteration of positive solution for a three-point boundary value problem with ap-Laplacian operator

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Abstract

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs

$$\left\{ \begin{gathered} (\phi _p (u\prime ))\prime + q(t)f(t, u) = 0,0< t< 1, \hfill \\ u(0) - B(u\prime (\eta )) = 0, u\prime (1) = 0 \hfill \\ \end{gathered} \right.$$

and

$$\left\{ \begin{gathered} (\phi _p (u\prime ))\prime + q(t)f(t, u) = 0,0< t< 1, \hfill \\ u\prime (0) = 0, u(1) + B(u\prime (\eta )) = 0 \hfill \\ \end{gathered} \right.$$

The main tool is the monotone iterative technique. Here, the coefficientq(t) may be singular att = 0,1.

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Authors and Affiliations

  1. Department of Mathematics and Physics, North China Electric Power University (Beijing), 102206, Beijing, China

    De-Xiang Ma

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  1. De-Xiang Ma
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Ma, DX. Existence and iteration of positive solution for a three-point boundary value problem with ap-Laplacian operator. J. Appl. Math. Comput. 25, 329–337 (2007). https://doi.org/10.1007/BF02832357

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  • DOI: https://doi.org/10.1007/BF02832357

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