Concepedia

Existence Theorems for First-Order Equations on Time Scales with Δ-Carathéodory Functions

Hugues Gilbert

Advances in Difference Equations · 2010 · 17 citations · 9 references

DOIFull text

Open access

Concepts

Abstract

This paper concerns the existence of solutions for two kinds of systems of first-order equations on time scales. Existence results for these problems are obtained with new notions of solution tube adapted to these systems. We consider the general case where the right member of the system is -Caratheodory and, hence, not necessarily continuous.

References

9

Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus

Stefan Hilger · Results in Mathematics · 1990 · 2K citations

, , +10

Expression of the Lebesgue <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mstyle mathvariant="normal"><mml:mi>Δ</mml:mi></mml:mstyle></mml:math>-integral on time scales as a usual Lebesgue integral; application to the calculus of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mstyle mathvariant="normal"><mml:mi>Δ</mml:mi></mml:mstyle></mml:math>-antiderivatives

Alberto Cabada, Dolores Rodríguez Vivero · Mathematical and Computer Modelling · 2006 · 161 citations

, , +5

Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling

Christopher C. Tisdell, Atiya Zaidi · Nonlinear Analysis · 2007 · 160 citations

, , +14

Basic properties of Sobolev's spaces on time scales

Ravi P. Agarwal, M. Victoria Otero‐Espinar, Kanishka Perera et al. · Advances in Difference Equations · 2006 · 89 citations · Full text

, , +5

Criterions for absolute continuity on time scales

Alberto Cabada, Dolores Rodríguez Vivero · The Journal of Difference Equations and Applications · 2005 · 87 citations

, , +6