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Existence of triple symmetric positive solutions for four-point boundary-value problem with one-dimensional p-Laplacian

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Abstract

In this paper, we consider the four-point boundary value problem for one-dimensional p-Laplacian

$$\bigl(\phi_{p}(u'(t))\bigr)'+q(t)f\bigl(t,u(t),u'(t)\bigr)=0,\quad t\in(0,1),$$

subject to the boundary conditions

$$u(0)-\beta u'(\xi)=0,\qquad u(1)+\beta u'(\eta)=0,$$

where φ p (s)=|s|p−2 s. Using a fixed point theorem due to Avery and Peterson, we study the existence of at least three symmetric positive solutions to the above boundary value problem. The interesting point is the nonlinear term f is involved with the first-order derivative explicitly.

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Authors and Affiliations

  1. Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, China

    Hanying Feng

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

    Hanying Feng & Weigao Ge

Authors
  1. Hanying Feng
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  2. Weigao Ge
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Correspondence to Hanying Feng.

Additional information

Supported by NNSF of China (10371006) and SRFDP of China (20050007011).

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Feng, H., Ge, W. Existence of triple symmetric positive solutions for four-point boundary-value problem with one-dimensional p-Laplacian. J. Appl. Math. Comput. 27, 325–337 (2008). https://doi.org/10.1007/s12190-008-0048-1

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  • DOI: https://doi.org/10.1007/s12190-008-0048-1

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