JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (9): 69-75.doi: 10.6040/j.issn.1671-9352.0.2016.506

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Positive solutions of a second order periodic problems with derivative terms

YAN Dong-liang   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2016-11-03 Online:2017-09-20 Published:2017-09-15

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Abstract: This paper shows the existence of positive solutions of the fully second-order periodic boundary value problem {u″(t)+au(t)=f(t,u(t),u'(t)), t∈［0,1］,u(0)=u(1), u'(0)=u'(1),where(π2)/42, f:［0,1］×R+×R→R+ is continuous. f(t,x,y) is superlinear growth on x and y and a Nagumo-type condition is presented. Under the conditions that the superlinear case, the Nagumo-type condition is restrict the growth of f on y. Our discussion is based on the fixed point index theory in cones.

Key words: positive solution, fixed point index theory, second-order boundary value problem

CLC Number: 

  • O175.8
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