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.

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

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