JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (12): 96-101.doi: 10.6040/j.issn.1671-9352.0.2023.003

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Existence of positive solutions for a class of second-order semi-positone problems with Dirichlet boundary conditions

LI Cunli   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2024-12-12

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Abstract: The existence of positive solutions for second-order semi-positone problem{-u″(t)=λ(f(u(t))+a(t)), t∈(0,1),u(0)=u(1)=0is studied, where λ is a positive parameter, a∈C(［0,1］, R), f∈C(［0,∞),［0,∞)). When f has a superlinear growth, we prove that there exists a constant λ*>0 such that the problem has a positive solution for 0<λ<λ*. The proof of the main results is based on a fixed point theorem in cones.

Key words: positive solution, semi-positone problem, Dirichlet boundary condition, fixed point theorem

CLC Number: 

  • O175.8
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