Oscillation Theorems for Differential Equations Involving Even Order Nonlinear Sturm–Liouville Operator
Keyword(s):
Abstract We are concerned with the oscillatory and nonoscillatory behavior of solutions of differential equations involving an even order nonlinear Sturm–Liouville operator of the form where α and β are distinct positive constants. We first give the criteria for the existence of nonoscillatory solutions with specific asymptotic behavior on infinite intervals, and then derive necessary and sufficient conditions for all solutions of (∗) to be oscillatory by eliminating all nonoscillatory solutions of (∗).
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