Extrapolation spaces and controllability of impulsive semilinear functional differential inclusions with infinite delay in Fréchet spaces

Abstract

In this article, we investigate some classes of semilinear impulsive functional differential inclusions with infinite delay. It is assumed that the linear part is possibly neither densely defined nor it satisfies the Hille–Yosida condition on a Banach space, namely the extrapolated space. Our approach is based on the theory of extrapolation spaces combined with a recent Frigon nonlinear alternative for multivalued admissible contractions in Fréchet spaces.

Keywords:

• Semilinear functional differential inclusions
• Mild solution
• Fixed point
• Controllability
• Extrapolation spaces
• Nondensely defined
• 2000 Mathematics subject classifications:
• 34G20
• 34K25