New Hille Type and Ohriska Type Criteria for Nonlinear Third-Order Dynamic Equations

Abstract

The objective of this paper is to derive new Hille type and Ohriska type criteria for third-order nonlinear dynamic functional equations in the form of a2(ζ)φα2a1ζφα1xΔ(ζ)ΔΔ+q(ζ)φαx(g(ζ))=0, on a time scale T, where Δ is the forward operator on T, α1, α2, α>0, and g, q, ai, i = 1, 2, are positive rd-continuous functions on T, and φθ(u):=uθ−1u. Our results in this paper are new and substantial for dynamic equations of the third order on arbitrary time scales. An example is included to illustrate the results.