Second-order periodic boundary value problems on time scales. (English) Zbl 1068.34016

Topal, S. Gulsan

Comput. Math. Appl. 48, No. 3-4, 637-648 (2004).

The author considers the existence of solutions of periodic boundary value problem for second-order nonlinear dynamic equations on time scales \[ -y^{\Delta\nabla}(t)+q(t)y(t)=f(t,y(t)),\quad t\in [a,b], \]
\[ y(\rho(a))=y(b),\quad y^\Delta(\rho(a))=y^\Delta(b), \] where \([a,b]\) is a subset of the time sale \(T\); \(h^\Delta(t)\) is the delta derivative of \(h\), \(h^\nabla(t)\) is the nabla derivative of \(h\).

Reviewer: Anatolij Ivan Kolosov (Khar’kov)

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
39A12	Discrete version of topics in analysis

Keywords:

delta derivative; nabla derivative; dynamic equations; Green’s function

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