Electron. J. Diff. Equ., Vol. 2011 (2011), No. 108, pp. 1-11.

Continuous solutions of distributional Cauchy problems

Seppo Heikkila

Existence of the smallest, greatest, minimal, maximal and unique continuous solutions to distributional Cauchy problems, as well as their dependence on the data, are studied. The main tools are a continuous primitive integral and fixed point results in function spaces.

Submitted February 28, 2011. Published August 25, 2011.
Math Subject Classifications: 26A24, 26A39, 34A12, 34A36, 47B38, 47H07, 58D25.
Key Words: Distribution; primitive integral; continuous; Cauchy problem; fixed point; smallest solution; greatest solution; minimal solution; maximal solution.

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Seppo Heikkilä
Department of Mathematical Sciences
University of Oulu, BOX 3000
FIN-90014 University of Oulu, Finland
email: sheikki@cc.oulu.fi

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