
Thirdorder periodic boundary value problems with signchanging Greens function
 CHEN Bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):
7983.
doi:10.6040/j.issn.16719352.0.2015.476

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We study the existence of positive solutions of nonlinear periodic boundary value problemsu(t)+a(t)u(t)=λb(t)f(u(t)), a.e t∈［0,2π］,u^{(i)}(0)=u^{(i)}(2π), i=0,1,2where a≺0, b≺0 and the Greens function of the linear problemu(t)+a(t)u(t)=0, a.e t∈［0,2π］,u^{(i)}(0)=u^{(i)}(2π), i=0,1,2may change sign on ［0,2π］×［0,2π］.