Vol. 38, No. 3, 1971

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Oscillatory properties of solutions of even order differential equations

Hiroshi Onose

Vol. 38 (1971), No. 3, 747–757
Abstract

Consider the following n-th order nonlinear differential equation

x(n) + f(t,x,x′,⋅⋅⋅ ,x(n−1)) = 0.
(1)

All functions considered will be assumed continuous and au the solutions of (1), continuously extendable throught the entire nonnegative real axis. A nontrivial solution of (1) is called oscillatory if it has zeros for arbitrarily large t and equation (1) is called oscillatory if all of its solutions are oscillatory. A nontrivial solution of (1) is called nonoscillatory if it has only a finite number of zeros on [t0,) and equation (1) is called nonoscillatory if all of its solutions are nonoscillatory. In this paper, theorems on oscillation and nonoscillation are presented.

Mathematical Subject Classification 2000
Primary: 34C10
Milestones
Received: 11 May 1970
Published: 1 September 1971
Authors
Hiroshi Onose