JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (12): 79-86.doi: 10.6040/j.issn.1671-9352.0.2023.038

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Existence of one-signed solutions for three-point boundary value problems of second-order differential equations

LIU Huijuan   

  1. School of Mathematics and Statistics, Xidian University, Xian 710126, Shaanxi, China
  • Published:2024-12-12

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Abstract: In this paper, we study the existence of one-signed solutions for three-point boundary value problems of nonlinear second-order differential equations{u″+a(t)f(u)=0, t∈［0,1］,u(0)=0, u(1)=u(ε)where ε∈(0,1), a∈C(［0,1］,(0,∞)), f∈C(R,R)with sf(s)>0 for s≠0, λ1 is the principal eigenvalue of the linear eigenvalue problem: u″+λa(t)u=0, u(0)=0, u(1)=u(ε), t∈［0,1］. Assume that either(λ1)/(f∞)<1<(λ1)/(f0) or (λ1)/(f0)<1<(λ1)/(f∞), the problem has at least one positive solution u(t) and one negative solution v(t). The proof of main results is based on bifurcation techniques.

Key words: second-order differential equation, three-point boundary value problem, Greens function, bifurcation technique, one-signed solution

CLC Number: 

  • O175.8
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