Geodesic
Oscillation Criteria for Second Order Nonlinear Differential Equations Involving Integral Averages
Canadian journal of mathematics, Tome 45 (1993) no. 5, pp. 1094-1103

Voir la notice de l'article provenant de la source Cambridge University Press

Consider the second order nonlinear differential equation y" + a(t)f(y) = 0where a(t) ∈ C[0,∞),f(y) GC 1 (-∞, ∞),ƒ'(y) ≥ 0 and yf(y) > 0 for y ≠ 0. Furthermore, f(y) also satisfies either a superlinear or a sublinear condition, which covers the prototype nonlinear function f(y) = |γ|γ sgny with γ > 1 and 0 < γ < 1 known as the Emden-Fowler case. The coefficient a(t) is allowed to be negative for arbitrarily large values of t. Oscillation criteria involving integral averages of a(t) due to Wintner, Hartman, and recently Butler, Erbe and Mingarelli for the linear equation are shown to remain valid for the general equation, subject to certain nonlinear conditions on f(y). In particular, these results are therefore valid for the Emden-Fowler equation.
DOI : 10.4153/CJM-1993-060-3
Mots-clés : 34C10, 34C15, second order, nonlinear, ordinary differential equations, oscillation, asymptotic behavior 
Wong, James S. W. Oscillation Criteria for Second Order Nonlinear Differential Equations Involving Integral Averages. Canadian journal of mathematics, Tome 45 (1993) no. 5, pp. 1094-1103. doi: 10.4153/CJM-1993-060-3
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