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,λ,is the principal eigenvalue of the linear eigen-value 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.
关键词
二阶微分方程/三点边值问题/格林函数/分歧理论/定号解
Key words
second-order differential equation/three-point boundary value problem/Green's function/bifurcation technique/one-signed solution
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