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Existence of positive solutions of Neumann boundary value problem via a cone compression-expansion fixed point theorem of functional type

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Abstract

This paper is devoted to study the existence of positive solutions of second-order boundary value problem

$$-u''+m^2u=h(t)f(t,u),\quad t\in (0,1)$$

with Neumann boundary conditions

$$u'(0)=u'(1)=0,$$

where m>0, f∈C([0,1]×ℝ+,ℝ+), and h(t) is allowed to be singular at t=0 and t=1. The arguments are based only upon the positivity of the Green function, a fixed point theorem of cone expansion and compression of functional type, and growth conditions on the nonlinearity f.

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Authors and Affiliations

  1. School of Mathematics and Physics, Jiangsu Polytechnic University, Changzhou, 213164, P.R. China

    Feng Wang & Fang Zhang

Authors
  1. Feng Wang
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  2. Fang Zhang
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Correspondence to Feng Wang.

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Research supported by the National Natural Science Foundation of China (10671167).

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Wang, F., Zhang, F. Existence of positive solutions of Neumann boundary value problem via a cone compression-expansion fixed point theorem of functional type. J. Appl. Math. Comput. 35, 341–349 (2011). https://doi.org/10.1007/s12190-009-0360-4

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  • DOI: https://doi.org/10.1007/s12190-009-0360-4

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