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The Stability of Solutions of Generalized Emden-Fowler Equations

Published online by Cambridge University Press:  20 November 2018

Hugo Teufel Jr
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Abstract

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This paper gives several monotonicity properties of all oscillatory solutions of equations with separable and nonseparable nonlinearities which are more general than the Emden- Fowler equations

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Principally, if x(t) is an oscillatory solution, conditions are given such that; if a(t)↑ ∞ as t → ∞, then x(t) → 0; and, if a(t) ↓ 0 as t → ∞, then lim sup | x(t) | = ∞.

Keywords

34C1034D99Emden-Fowler equationoscillationmonotonicitystabilityconvexity
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 3 , 01 September 1974 , pp. 397 - 401
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Burton, T. and Grimmer, R., On the asymptotic behavior of solutions of x″ + a(t)f(x)=0, Proc. Camb. Phil. Soc. 70 (1971), 77-88.Google Scholar
2. Das, K., Comparison and monotonity theorems for second order non-linear differential equations, Acta. Math. Sci. Hungar. 15 (1964), 449-456.Google Scholar
3. DeKleine, H. A., A counterexample to a conjecture in second-order linear equations, Mich. Math. J. 17 (1970), 29-32.Google Scholar
4. Hartman, P., The existence of large or small solutions of linear differential equations, Duke Math. J. 28 (1961), 421-430.Google Scholar
5. Heidel, J. W. and Hinton, D. B., The existence of oscillatory solutions for a nonlinear differential equation (to appear).Google Scholar
6. Hinton, D. B., Some stability conditions for a nonlinear differential equation, Trans. Amer. Math. Soc. 139 (1969), 349-358.Google Scholar
7. Chiou, Kuo-liang, A second order nonlinear oscillation theorem, SIAM J. Appl. Math. 21 (1971).Google Scholar
8. Wong, J. S. W., On the global asymptotic stability of(p(t)x/′)′+q(t)x2n-1=0 , J. Inst. Maths. Applies. 3 (1967), 403-05.Google Scholar
9. Wong, J. S. W., On second order nonlinear oscillation, Funkc. Ekvac. 11 (1969), 207-234.Google Scholar