Interval criteria for oscillation of second-order self-adjoint impulsive differential equations

Sugie, Jitsuro

doi:10.1090/proc/14797

Interval criteria for oscillation of second-order self-adjoint impulsive differential equations
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Proc. Amer. Math. Soc. 148 (2020), 1095-1108 Request permission

Abstract:

In this paper, oscillation theorems are given for second-order self-adjoint impulsive differential equations. The obtained results extend the well-known Kamenev-type and Philos-type oscillation theorems. A generalized Riccati transformation is used to prove these results. There are two advantages of using the generalized Riccati transformation rather than the standard Riccati transformation. One is that Kamenev-type and Philos-type oscillation theorems cannot be applied to conditionally oscillatory differential equations such as Euler’s equations, but the obtained results can be applied even to such equations. The other advantage is the ability to prove that the impulsive differential equation may become oscillatory even if the total impulse is small. A specific example is included to demonstrate the merits of the results obtained.

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