Oscillation Theory for Functional Differential Equations
Examines developments in the oscillatory and nonoscillatory properties of solutions for functional differential equations, presenting basic oscillation theory as well as recent results. The book shows how to extend the techniques for boundary value problems of ordinary differential equations to those of functional differential equations.
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Applications Assume assumptions Banach space becomes boundary value problem bounded positive solution bounded solution characteristic equation Choose Clearly closed compact condition consider constant continuous functions contraction contradicts convergence Corollary defined delay differential equations denote discuss easy equation z(t equicontinuous eventually positive solution Example exists exists a sequence fact fixed point theorem following result give given hand Hence holds implies inequality initial Integrating interval Lemma let z(t lim inf lim sup lim z(t linear negative neutral differential equation nondecreasing nonlinear nonoscillatory solution norm Noting obtain obvious operator oscillation oscillatory oscillatory solution positive solution z(t Proof proof of Theorem prove real root Remark respectively satisfies similar sint solution of Eq Substituting sufficiently large Suppose Theory Ti(t true Zhang