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Positive solutions and eigenvalue intervals for nonlinear systems

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Abstract

This paper deals with the existence of positive solutions for the nonlinear system

$$ (q(t)\phi (p(t)u'_i (t)))' + f^i (t,u) = 0, 0 < t < 1, i = 1,2, \ldots ,n $$

. This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here u = (u 1, …, u n) and f i, i = 1, 2, …, n are continuous and nonnegative functions, p(t), q(t): [0, 1] → (0, ∞) are continuous functions. Moreover, we characterize the eigenvalue intervals for

$$ (q(t)\phi (p(t)u'_i (t)))' + \lambda h_i (t)g^i (u) = 0, 0 < t < 1, i = 1,2, \ldots ,n $$

. The proof is based on a well-known fixed point theorem in cones.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100 084, China

    Jifeng Chu & Meirong Zhang

  2. Department of Applied Mathematics, Hohai University, Nanjing, 210 098, China

    Jifeng Chu

  3. Department of Mathematics, National University of Ireland, Galway, Ireland

    Donal O’regan

Authors
  1. Jifeng Chu
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  2. Donal O’regan
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  3. Meirong Zhang
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Chu, J., O’regan, D. & Zhang, M. Positive solutions and eigenvalue intervals for nonlinear systems. Proc Math Sci 117, 85–95 (2007). https://doi.org/10.1007/s12044-007-0007-z

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  • DOI: https://doi.org/10.1007/s12044-007-0007-z

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