%A WANG Jing-jing, LU Yan-qiong
%T Existence of optimal positive solutions for Neumann boundary value problems of second order differential equations
%0 Journal Article
%D 2020
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2019.208
%P 113-120
%V 55
%N 3
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_3248.shtml}
%8
%X 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 Greens 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@).