Oscillation Criteria for Second Order Nonlinear Differential Equations Involving General Means
- Wong, James S.W.
DOIAbstract
AbstractConsider the second order nonlinear differential equation (E) y″+a(t)f(y)=0 where a(t)∈C[0,∞), f(y)∈C1(−∞,∞), f′(y)≥0, and yf(y)>0 for y≠0. Furthermore, f(y) also satisfies either a superlinear or a sublinear condition, which covers the nonlinear function f(y)=y|y|γ−1 with γ>1 and 0<γ<1, respectively, commonly known as the Emden–Fowler case. Here the coefficient function a(t) is allowed to be negative for arbitrarily large values of t. Kamenev type oscillation criteria involving integral averages for the linear equations (L) y″+a(t)y=0 are extended to the nonlinear equation (E) by using more general means. The results extend similar results on general means by Philos for the linear equation (L) and also results based upon Kamenev's ...
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