Abstract
For the equation
minimal sufficient conditions ensure the existence of a nonoscillatory solution.L n is a disconjugate differential operator of the form
.
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Kusano, T. andNaito,Boundedness of solutions of a class of higher order ordinary differential equations. J. Differential Equations, to appear.
Lovelady, D. L.,On the oscillatory behavior of bounded solutions of higher order differential equations. J. Differential Equations19 (1975), 167–175.
Onose, H.,Oscillatory property of ordinary differential equations of arbitrary order. J. Differential Equations7 (1970), 454–458.
Philos, Ch. G.,On the oscillatory and asymptotic behavior of the bounded solutions of differential equations with deviating arguments. Ann. Mat. Pura Appl.119 (1979), 25–40.
Philos, Ch. G. andStaikos, V. A.,Boundedness and oscillation of solutions of differential equations with deviating argument. An Ştiinţ. Univ. “Al. I. Cuza” Iaşi Secţ. I a Mat. (N.S.)26 (1980), no. 2, 307–317.
Singh, Bhagat,Necessary and sufficient condition for maintaining oscillations and nonoscillations in general functional equations and their asymptotic properties. SIAM J. Math. Anal.10 (1979), 18–31.
Singh, Bhagat,A necessary and sufficient condition for the oscillation of an even order nonlinear delay differential equation. Canad. J. Math.25 (1973), 1078–1089.
Singh, Bhagat andKusano, T.,On asymptotic limits of nonoscillations in functional equations with retarded arguments. Hiroshima Math. J.10 (1980), 557–565.
Singh, Bhagat andKusano, T.,Asymptotic behavior of oscillatory solutions of a differential equation with deviating arguments. J. Math. Anal. Appl.83 (1981), 395–407.
Trench, W. F.,Canonical forms and principal systems for general disconjugate equations. Trans. Amer. Soc.189 (1973), 319–327.
Trench, W. F.,Oscillation properties of perturbed disconjugate equations. Proc. Amer. Math. Soc.52 (1975), 147–155.
Willett, D.,Asymptotic behavior of disconjugate nth order differential equations. Canad. J. Math.23 (1971), 293–314.
Yeh, Cheh C.,An oscillation criterion for second order nonlinear differential equations with functional arguments. J. Math. Anal. Appl.76 (1980), 72–76.
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Singh, B. On existence of nonoscillatory solutions in forced nonlinear differential equations. Aeq. Math. 29, 150–161 (1985). https://doi.org/10.1007/BF02189823
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DOI: https://doi.org/10.1007/BF02189823