What question did this study set out to answer?

The research aims to explore the properties of unbounded solutions in a specific class of fourth order dynamic equations.

April 10, 2026Open Access

Properties of an Unbounded Solutions of a Fourth Order Neutral Dynamic Equations

Key Points

The research aims to explore the properties of unbounded solutions in a specific class of fourth order dynamic equations.
Analysis of the form of fourth order dynamic equations involving various functions and integral conditions.
Examination of unbounded solutions under assumptions related to time scales.
Evaluation of integral conditions that determine the behavior of solutions.
Establishment of the conditions under which solutions can be deemed unbounded.
Identification of specific ranges of functions that affect the properties of solutions effectively.

Abstract

In this paper, the author studied, the properties of an unbounded solutions of a class of fourth order dynamic equation of the form\ (r (t) (x (t) +p (t) x (α (t) ) ) ^ (∆²) ) ^ (∆²) +g (t) G (x (β (t) ) ) -h (t) H (x (γ (t) ) ) =0 (H) \ 〖t∈[t₀, ┤ ├ ∞) 〗T where 𝕋 is a time scale with⁡sup⁡〖T=+∞〗, t₀ (≥0) ∈T are studied under the assumption\₀ ∫_ (t₀) ^∞▒〖t/ (r (t) ) ∆t=∞ 〗and ( (〖H₀〗^\\\' ∫_ (t₀) ^∞▒〖t/r (t) ∆t<∞〗 for various ranges of p (t). \

Properties of an Unbounded Solutions of a Fourth Order Neutral Dynamic Equations

Key Points

Abstract

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