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Uniqueness of positive solutions for a class of fourth-order boundary value problems. (English) Zbl 1222.34027

Summary: The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fourth-order boundary value problem:

y (4) (t)=f(t,y(t)),t[0,1],y(0)=y(1)=y ' (0)=y ' (1)=0·

Moreover, under certain assumptions, we prove that the above boundary value problem has a unique symmetric positive solution. Finally, we present some examples and compare our results with the ones obtained in recent papers. Our analysis relies on a fixed-point theorem in partially ordered metric spaces.

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