JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (4): 89-96.doi: 10.6040/j.issn.1671-9352.0.2022.261

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Existence of positive solutions for a class of second order semipositone problems

SHI Xuan-rong   

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

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Abstract: The existence of positive solutions for the second order semipositone problem{-u″(t)=λh(t)f(u(t)), t∈(0,1),αu(0)-b(u'(0))u'(0)=0, c(u(1))u(1)+δu'(1)=0 is studied, where λ is a positive parameter,α,δ>0 are constants,b,c∈C(［0,∞),［0,∞)),h∈C(［0,1］,［0,∞)), f∈C(［0,∞),R), f >-M(M>0)and f∞:=limx→∞(f(x))/x=∞。The proof of the main theorems is based on fixed point theorem of Krasnoselskii.

Key words: positive solution, semipositone problem, existence, Krasnoselskii fixed point theorem

CLC Number: 

  • O175.8
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