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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

  • Li Ren-gui
  • Liu Li-shan
Article
  • 23 Downloads

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≤f 0 + <M1, m1<f ≤∞ or 0≤f + <M1, m1<f 0 ≤∞, where\(\begin{gathered} f_0^ + = \overline {\lim } _{u \to 0} f(u)/u, f_\infty ^ - = \underline {\lim } _{u \to \infty } f(u)/u, f_0^ - = \hfill \\ \underline {\lim } _{u \to 0} f(u)/u, f_\infty ^ + = \overline {\lim } _{u \to \infty } f(u)/u \hfill \\ \end{gathered} \), g may be singular at t=0 and/or t=1. The proof uses a fixed point theorem in cone theory.

Key words

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

CLC number

O175.8 

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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.zbMATHMathSciNetCrossRefGoogle Scholar
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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

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

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