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Displaying 41 –
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Consider the third order nonlinear dynamic equation
, (*)
on a time scale which is unbounded above. The function f ∈ C(,) is assumed to satisfy xf(x) > 0 for x ≠ 0 and be nondecreasing. We study the oscillatory behaviour of solutions of (*). As an application, we find that the nonlinear difference equation
,
where α ≥ -1, γ > 0, c > 3, is oscillatory.
In this paper we prove existence theorems for integro - differential equations
,
t ∈ Iₐ = [0,a] ∩ T, a ∈ R₊,
x(0) = x₀
where T denotes a time scale (nonempty closed subset of real numbers R), Iₐ is a time scale interval. Functions f,k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral.
Additionally, functions f and k satisfy some boundary conditions and conditions...
Currently displaying 41 –
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121