On the solvability of distributional and impulsive systems of Cauchy problems

DOI10.1016/J.NA.2012.04.031zbMath1258.34024OpenAlexW1978532561MaRDI QIDQ435881

Seppo Heikkilä

Publication date: 12 July 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.04.031

zbMATH Keywords

impulsive differential equationexistence and uniqueness of solutionscontinuous dependencedistributional Cauchy problemdistributional differential equationimpulsive Cauchy problemminimal and maximal solutionprimitive integralsmallest and greatest solution

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Ordinary differential equations with impulses (34A37) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Fixed-point theorems (47H10) Discontinuous ordinary differential equations (34A36) Denjoy and Perron integrals, other special integrals (26A39)

Related Items (3)

Extremal solutions of measure differential equations ⋮ The continuous primitive integral in the plane ⋮ Well-posedness results for abstract generalized differential equations and measure functional differential equations

Cites Work

• On singular nonlinear distributional and impulsive initial and boundary value problems
• The regulated primitive integral
• On nonlinear distributional and impulsive Cauchy problems
• The distributional Denjoy integral
• Uniqueness and existence results for implicit impulsive differential equations
• Fixed Point Theory in Ordered Sets and Applications
• Linear distributional differential equations in the space of regulated functions
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