PHILOS-TYPE OSCILLATION CRITERIA FOR SECOND ORDER HALF-LINEAR DYNAMIC EQUATIONS ON TIME SCALES

PHILOS-TYPE OSCILLATION CRITERIA FOR SECOND ORDER HALF-LINEAR DYNAMIC EQUATIONS ON TIME SCALES

In this paper we establish some oscillation theorems for the second order half-linear dynamic equation (r(t)(xΔ(t))ϒ)Δ + p(t)xϒ(t) = 0, t ∈ [a, b], on time scales. Special cases of our results include some well-known oscillation results for second-order differential and half-linear differential equa...

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Veröffentlicht in:The Rocky Mountain journal of mathematics 2007-01, Vol.37 (4), p.1085-1104
Hauptverfasser: AGARWAL, RAVI P., O'REGAN, DONAL, SAKER, S.H.
Format: Artikel
Sprache:eng
Schlagworte:
34C10
34K11
93C70
Continuous functions
Difference equations
Differential equations
Euler equations
Integers
Mathematical theorems
Oscillation
Second order differential equations
second order half-linear dynamic equations
Sufficient conditions
time scale
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Beschreibung
Zusammenfassung:In this paper we establish some oscillation theorems for the second order half-linear dynamic equation (r(t)(xΔ(t))ϒ)Δ + p(t)xϒ(t) = 0, t ∈ [a, b], on time scales. Special cases of our results include some well-known oscillation results for second-order differential and half-linear differential equations. Our results are new for difference, generalized difference and q difference half-linear equations.
ISSN:0035-7596
1945-3795
DOI:10.1216/rmjm/1187453098