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We consider establishing lower bounds for the first zero of the solution of the nonlinear second order initial value problem (p(x)y′(x))′ + f (x,y(x)) = 0, x 0 y(0) = a > 0, y′(0) = 0. Using the linear case as a starting point, we prove several of these theorems, comparing them by considering several examples. Mathematics subject classification (2010): 34C10, 34A34, 34A36.

Lower bounds for the first zero for nonlinear second order differential equations