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On the solvability of distributional and impulsive systems of Cauchy problems

Authors :
Seppo Heikkilä
Source :
Nonlinear Analysis: Theory, Methods & Applications. 75:4604-4631
Publication Year :
2012
Publisher :
Elsevier BV, 2012.

Abstract

In this paper, existence results are derived for the unique, smallest, greatest, minimal, and/or maximal solutions of finite systems of nonlinear distributional Cauchy problems. The dependence of solutions on the data is also studied. Applications to systems of distributional differential equations with impulses and to higher-order distributional Cauchy problems are presented. The main tools are fixed point results in function spaces and a primitive integral of distributions defined in the paper, including recently introduced regulated and continuous primitive integrals on compact intervals.

Details

ISSN :
0362546X
Volume :
75
Database :
OpenAIRE
Journal :
Nonlinear Analysis: Theory, Methods & Applications
Accession number :
edsair.doi...........746aa94f806940bd0eb69197a48bb9d1