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- W2101893160 abstract "In this paper we examine the dynamic equation (p(t)x (t)) r + q(t)x(t) = 0 on a time scale. Little work has been done on this equation, which combines both the delta and nabla derivatives. Several preliminary results are established, including Abel's formula and its converse. We then proceed to investigate oscillation and disconjugacy of this dynamic equation. AMS (MOS) Subject Classication. 39A10. 1. NABLA DERIVATIVES In this paper, we are concerned with the second-order self-adjoint dynamic equa- tion (p(t)x ) r +q(t)x = 0: We begin our work by reviewing some properties of the nabla derivative, and then in Section 2, we proceed to establish several results concerning the interaction of the two types of derivatives. In the third section of the paper, we develop Abel's formula, and its converse, which we then use to prove a reduction of order theorem. In the nal section, we turn our attention to oscillation and disconjugacy, establishing rst an analogue of the Sturm separation theorem, and then, via the P olya and Trench factorizations, we demonstrate the existence of recessive and dominant solutions of the self-adjoint equation. Here it is assumed that the reader is already familiar with the basic notions of" @default.
- W2101893160 created "2016-06-24" @default.
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- W2101893160 date "2003-01-01" @default.
- W2101893160 modified "2023-09-27" @default.
- W2101893160 title "A SECOND-ORDER SELF-ADJOINT EQUATION ON A TIME SCALE" @default.
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