Existence results for solutions to discontinuous dynamic equations on time scales

DOI10.7153/dea-2020-12-06zbMath1465.34104OpenAlexW3010748472MaRDI QIDQ5857942

Iguer Luis Domini dos Santos, Sanket Tikare

Publication date: 8 April 2021

Published in: Differential Equations & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/dea-2020-12-06

zbMATH Keywords

existence of solutionstime scalesfixed point theoremdynamic equationsCarathéodory function

Mathematics Subject Classification ID

Applications of operator theory to differential and integral equations (47N20) Discontinuous ordinary differential equations (34A36) Dynamic equations on time scales or measure chains (34N05)

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Cites Work

• On qualitative and quantitative results for solutions to first-order dynamic equations on time scales
• Existence theorems for first-order equations on time scales with \(\Delta \)-Carathéodory functions
• Dynamic equations on time scales and generalized ordinary differential equations
• Discontinuous dynamic equations on time scales
• Integration on time scales.
• Absolute continuity and existence of solutions to dynamic inclusions in time scales
• Expression of the Lebesgue \(\Delta\)-integral on time scales as a usual Lebesgue integral; application to the calculus of \(\Delta\)-antiderivatives
• A Cauchy Problem on Time Scales with Applications
• General Cauchy–Lipschitz theory for Δ-Cauchy problems with Carathéodory dynamics on time scales
• Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals
• Qualitative analysis of dynamic equations on time scales
• On the existence and uniqueness of solutions to dynamic equations
• Boundedness and Uniqueness of Solutions to Dynamic Equations on Time Scales
• Generalized first order dynamic equations on time scales with Δ-Carathéodory functions
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