We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem y″″=λa（x）f（y）,0〈x〈1,y（0）=y（1）=y″（0）=y″（1）=0where λ is a positive parameter, a ∈ C（[0, 1], （0, ∞）, f ∈C（R,R） satisfies f（u）u 〉 0 for all u ≠ 0. We give conditions on the ratio f（s）/s, at infinity and zero, that guarantee the existence of nodal solutions.The proof of our main results is based upon bifurcation techniques.
该文运用锥上的不动点定理研究非线性二阶常微分方程无穷多点边值问题u″+α(t)f(u)=0,t∈(0,1), u(0)=0,u(1)=sum from i=1 to∞(α_iu(ξ_i)正解的存在性。其中ξ_i∈(0,1),α_i∈[0,∞),且满足sum from i=1 to∞(α_iξ_i)<1.a∈C([0,1],[0,∞)),f∈C([0,∞),[0,∞)).
