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

LI Ren-gui; LIU Li-shan

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LI Ren-gui, LIU Li-shan. Positive Solutions of Boundary Value Problems for Second Order Singular Nonlinear Differential Equations[J]. Applied Mathematics and Mechanics, 2001, 22(4): 435-440.

Citation:

LI Ren-gui, LIU Li-shan. Positive Solutions of Boundary Value Problems for Second Order Singular Nonlinear Differential Equations[J]. Applied Mathematics and Mechanics, 2001, 22(4): 435-440.

Citation:

LI Ren-gui, LIU Li-shan. Positive Solutions of Boundary Value Problems for Second Order Singular Nonlinear Differential Equations[J]. Applied Mathematics and Mechanics, 2001, 22(4): 435-440.

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

Department of Mathematics, Qufu Normal University, Qufu, Shangdong 273165, P R China

Received Date: 2000-01-17
Rev Recd Date: 2000-03-03
Publish Date: 2001-04-15

Abstract

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≤f₀⁺<M₁,m₁<f_∞^-≤∞ or 0≤f_∞⁺<M₁,m₁<f₀^-≤∞,where f₀⁺=₀f(u)/u,f_∞^-=_∞f(u)/u,f₀^-=₀f(u)/u,f_∞⁺=_∞f(u)/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(4)

References

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