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Set differential equations in Frechet spaces

Galanis G., N., Bhaskar T., G., Lakshmikantham V.

Journal of Applied Analysis

2008

Vol. 14, nr 1

103-113

It is known that a frachet space F can be realized as a projective limit of a sequence of Banach spaces Ei. The space Kc(F) of all compact, convex subsets of a Frechet space, F, is realized as a projective limit of the semilinear metric spaces Kc(Ei). Using the notion of Hukuhara derivative for maps with values in Kc(F), we prove the local and global existence theorems for an initial value problem associated with a set differential equation.

An existence theorem for set differential inclusions in a semilinear metric space

De Blasi F. S., Lakshmikantham V., Bhaskar T. G.

Control and Cybernetics

2007

Vol. 36, no 3

571-582

Using the notion of continuous approximate selections, we establish an existence theorem for set differential inclusions in a semi-linear metric space.

Maximal solutions and existence theory for fuzzy differential and integral equations

Agarwal R. P., O'Regan D., Lakshmikantham V.

Journal of Applied Analysis

2005

Vol. 11, nr 2

171-186

New existence resilts are prosented for fuzzy differential and integral equations. Our analysis combines the stacking theorem with results concerning the maximal solution for an appropriate differential equation.