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Positive solutions of nonlinear second-order Neumann boundary value problems with a variable coefficient

YAO Qing-liu   

  1. Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, Jiangsu, China
  • Received:1900-01-01 Revised:1900-01-01 Online:2006-10-24 Published:2006-10-24
  • Contact: YAO Qing-liu

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Abstract: Neumann boundary value problems describe many physical phenomena whose gradients are zero at boundary points. The positive solutions of nonlinear second-order Neumann boundary value problem u″(t)+k(t)u(t)=f(t,u(t)), 0≤t≤1, u′(0)=u′(1)=0 with function coefficient k(t)were studied by applying the fixed-point index theorem of cones. The main results show that the problem has n positive solutions provided growth rates of nonlinear term on　some bounded sets are appropriate, where n is an arbitrary natural number.

Key words: multiplicity , existence, positive solution, Neumann boundary value problem, nonlinear ordinary differential equation

CLC Number: 

  • O175.8
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