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## ftp ejde.math.txstate.edu FREDHOLM TYPE INTEGRODIFFERENTIAL EQUATION ON TIME

### Citations

39 | Ostrowski inequalities on time scales,
- BOHNER, MATTHEWS
- 2008
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Citation Context ...r s, t ∈ Z with s < t, where α = −1 is a constant and p : Z → R is a sequence satisfying p(t) = −1 for all t ∈ Z. We use the following fundamental result proved in Bohner and Peterson [1] (see also =-=[3]-=-). Lemma 2.1. Suppose u, b ∈ Crd and a ∈ ℜ + . Then u ∆ (t) ≤ a(t)u(t) + b(t) (2.8) for all t ∈ T, implies ∫ t u(t) ≤ u(t0)ea(t, t0) + ea(t, σ(τ))b(τ)∆τ, (2.9) for all t ∈ T. 3. Basic integral inequal... |

23 |
Dynamic equations on time scales. Birkhauser Boston Inc.,
- Bohner, Peterson
- 2001
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Citation Context ...τ ≤ t and IT = I ∩ T, I = [t0, ∞) the given subset of R, Rn the real n-dimensional Euclidean space with appropriate norm defined by | · |. The integral sign represents the delta integral. Recently in =-=[1, 2, 5, 7, 8, 9, 10]-=- the authors have studied the existence, uniqueness and other qualitative properties of solutions of various dynamic equations on time scales by using different techniques. In fact the study of equati... |

14 |
Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling, Nonlinear Anal.
- Tisdell, Zaidi
- 2008
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Citation Context ...Stefan Hilger [4] in 1988 which unifies continuous and discrete analysis. Since then many authors have studied various aspects of dynamic integral equations on time scales by using various techniques =-=[5, 7, 8, 9, 10]-=-. In this paper we consider the integrodifferential equation x ∆ (t) = f(t, x(t), x ∆ (t), Hx(t)), x(α) = x0, (1.1) for t ∈ [α, β] ⊂ IT, where ∫ β Hx(t) = h(t, τ, x(τ), x ∆ (τ))∆τ, (1.2) α f, h are gi... |

9 | Volterra integral equations on time scales: basic qualitative and quantitative results with applications to initial value problems on unbounded domains,”
- Kulik, Tisdell
- 2008
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Citation Context ...Stefan Hilger [4] in 1988 which unifies continuous and discrete analysis. Since then many authors have studied various aspects of dynamic integral equations on time scales by using various techniques =-=[5, 7, 8, 9, 10]-=-. In this paper we consider the integrodifferential equation x ∆ (t) = f(t, x(t), x ∆ (t), Hx(t)), x(α) = x0, (1.1) for t ∈ [α, β] ⊂ IT, where ∫ β Hx(t) = h(t, τ, x(τ), x ∆ (τ))∆τ, (1.2) α f, h are gi... |

5 |
Analysis on Measure chain-A unified approch to continuous and discrete calculus, Results
- Hilger
- 1990
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Citation Context ...n time scales. A new integral inequality with explicit estimate on time scales is obtained and used to establish the results. 1. Introduction The theory of time scales was introduced by Stefan Hilger =-=[4]-=- in 1988 which unifies continuous and discrete analysis. Since then many authors have studied various aspects of dynamic integral equations on time scales by using various techniques [5, 7, 8, 9, 10].... |

5 | Pachpatte; Integral and Finite Difference Inequalities and Applications - G - 2006 |

3 |
Successive approximations to solutions of dynamic equations on time scales
- Tisdell, Zaidi
(Show Context)
Citation Context ...Stefan Hilger [4] in 1988 which unifies continuous and discrete analysis. Since then many authors have studied various aspects of dynamic integral equations on time scales by using various techniques =-=[5, 7, 8, 9, 10]-=-. In this paper we consider the integrodifferential equation x ∆ (t) = f(t, x(t), x ∆ (t), Hx(t)), x(α) = x0, (1.1) for t ∈ [α, β] ⊂ IT, where ∫ β Hx(t) = h(t, τ, x(τ), x ∆ (τ))∆τ, (1.2) α f, h are gi... |

1 |
Pachpatte; Properties of solutions to nonlinear dynamic integral equations on time scales
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Pachpatte; On Nonstandard Volterra type dynamic integral equations on time scales, Electronic Journal of Qualitative theory of differential equations
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