JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (3): 113-120.doi: 10.6040/j.issn.1671-9352.0.2019.208

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Existence of optimal positive solutions for Neumann boundary value problems of second order differential equations

WANG Jing-jing, LU Yan-qiong*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-03-27

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Abstract: By using the fixed point exponential theory of cone mapping, we show the optimal conditions for the existence of positive solutions for second-order continuous Neumann boundary value problems {u″(t)+a(t)u(t)=g(t)f(u(t)), t∈［0,T］,u'(0)=u'(T)=0with nonnegative Greens function, where f∈C(R+,R+), a(·)∈C(［0,T］,(0,+SymboleB@))satisfying the corresponding homogeneous linear problems have only trivial solutions, g∈C((0,T),R+), and g(t) is allowed to be singular at t=0 and t=T, R+:=［0,SymboleB@).

Key words: Neumann boundary value problem, positive solution, nonnegative Greens function, fixed point exponent

CLC Number: 

  • O175.8
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