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Existence of positive solutions of a nonlinear fourth-order boundary value problem. (English) Zbl 1195.34037

Summary: We study the existence of positive solutions of fourth-order boundary value problem

u (4) (t)=f(t,u(t),u '' (t)),t(0,1)·
u(0)=u(1)=u '' (0)=u '' (1)=0,

where f:[0,1]×[0,)×(-,0][0,) is continuous. The proof of our main result is based upon the Krein-Rutman theorem and the global bifurcation techniques.

MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
47J15Abstract bifurcation theory
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