JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (6): 64-69.doi: 10.6040/j.issn.1671-9352.0.2017.178

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Existence of positive solutions for a class of nonlinear second-order Dirichlet problem

  

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2017-04-20 Online:2018-06-20 Published:2018-06-13

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Abstract: The existence of positive solutions for a class of second-order Dirichlet problem{u″(t)+a(t)u(t)+f(t,u(t))=0, t∈(0,1),u(0)=u(1)=0is studied by using the fixed-point theorem in cones, where a∈C(［0,1］, ［0,∞))and a(t)≢0 on any subinterval of(0,1), f∈C(［0,1］×［0,∞), ［0,∞)). The results generalize and improve the related results of the existingwork.

Key words: Green function, existence, positive solutions, Dirichlet problem

CLC Number: 

  • O175.8
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