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Opial's inequality and oscillation of 2nd order equations

Author(s): R. C. Brown; D. B. Hinton
Journal: Proc. Amer. Math. Soc. 125 (1997), 1123-1129.
MSC (1991): Primary 34C10; Secondary 34L05, 34L15
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Abstract: For a second-order differential equation, we obtain from Opial's inequality lower bounds for the spacing between two zeros of a solution or between a zero of a solution and a zero of its derivative. These bounds are expressed in terms of antiderivatives of the potential, and in particular we derive some new Liapunov type inequalities from them.

References:

1.: P. R. Beesack and K.M. Das, Extensions of Opial's inequality, Pacific J. Math. 26 (1968), 215-232. MR 39:385
2.: D. W. Boyd, Best constants in a class of integral inequalities, Pacific J. Math. 30 (1969), 367-383. MR 40:2801
3.: B. J. Harris and Q. Kong, On the oscillation of differential equations with an oscillatory coefficient, Trans. Amer. Math. Soc. 347 (1995), 1831-1839. MR 95h:34050
4.: D. S. Mitrinovi\'{c}, J.E. P\v{e}cari\'{c}, and A.M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publishers, Dordrecht, 1991. MR 93m:26036


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