JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (4): 82-88.doi: 10.6040/j.issn.1671-9352.0.2022.222

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Existence of positive solutions for a class of semipositone second order Neumann boundary value problems

LEI Xiang-bing   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2023-03-27

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Abstract: This paper considers the existence of positive solutions of second order Neumann boundary value problems{u″(t)+a(t)u(t)=λf(t,u(t)), 0where λ is a positive parameter, a∈C［0,1］ and 0π2)/4, f∈C(［0,1］×R+,R)and f(t,0)<0. The proof of that there exists a positive constant λ0 such that the problem has one positive solution for 0<λ<λ0. The proof of the main results is based on topological degree theory.

Key words: Neumann boundary value problem, positive solution, semipositone, topological degree

CLC Number: 

  • O175.8
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