Solution Properties on Discrete Time Scales

Abstract

Dedicated to Allan Peterson on the occasion of his 60th birthday.

In this paper, we explore the solution properties of u ^{Δ 2} (t) + p(t)u ^γ(σ(t)) = 0 on a time scale 𝕋 with only isolated points, where p(t) is defined on 𝕋 and γ is a quotient of odd positive integers. Oscillation, nonoscillation, and solution comparisons, all depending on the sign of p, are included.

Keywords:

• Time scale
• Oscillation
• Discrete time scales
• Nonoscillatory

AMS Subject Classifications:

• 39A13
• 93C70