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Applied Mathematics and Mechanics

, Volume 22, Issue 4, pp 495–500 | Cite as

Positive Solutions of Boundary Value Problems for Second-Order Singular Nonlinear Differential Equations

  • Ren-gui Li
  • Li-shan Liu
Article

Abstract

New existence results are presented for the singular second-order nonlinear boundary value problems u″ + g(t)f(u) = 0, 0 < t < 1, αu(0) − βu′ (0) = 0, γu(1) + δu′(1) = 0 under the conditions\(0 \leqslant f_0^ + < M_1 ,m_1 < f_\infty ^ - \leqslant \infty {\text{ }}or{\text{ 0}} \leqslant f_\infty ^ + < M_1 ,m_1 < f_0^ - \leqslant \infty\), where\(f_0^ + = \overline {\lim } _{u \to 0} f\left( u \right)/u,f_\infty ^ - = \underline {\lim } _{u \to \infty } f\left( u \right)/u,f_0^ - = \underline {\lim } _{u \to 0} f\left( u \right)/u,f_\infty ^ + = \overline {\lim } _{u \to \infty } f\left( u \right)/u,\)g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory.

second-order singular boundary value problems positive solutions cone fixed point 

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References

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    Erbe L H, WANG Hai-yan. On the existence of positive solutions of ordinary differential equations[J]. Proc Amer Math Soc,1994,120(3):743-748.Google Scholar
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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Ren-gui Li
    • 1
  • Li-shan Liu
    • 1
  1. 1.Department of MathematicsQufu Normal UniversityQufuP R China

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