Summary: | We present a Dancer-type unilateral global bifurcation result for a class of fourth-order two-point boundary value problem x""+kx" +lx = λh(t)x+g(t, x,λ),0<t<1,x(0) = x(1) =x'(0)=x'(1)=0. Under some natural hypotheses on the perturbation function g: (0,1) ×R2 →R, we show that (λk,0) is a bifurcation point of the above problem. And there are two distinct unbounded continuas, and ,consisting of the bifurcation branch Ck from (λk,0),where λk is the k-th eigenvalue of the linear problem corresponding to the above problems. As an application of the above result,the global behavior of the components of nodal solutions of the following problem x"" + kx" +lx = rh(t) f(x) , 0<t<1, x(0)=x(1)=x'(0) = x'(1)=0 is studied. We obtain the existence of multiple nodal solutions for the problem if f0 =∞, f∞ ∈ (0,∞),.
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