Abstract
The goal of this paper is to show that some classes of partial differential functional equations admit a natural formulation as ordinary functional differential equations in infinite dimensional Banach spaces. Moreover, the equations thus obtained are driven by continuous right-hand sides satisfying the compactness assumptions required by the infinite-dimensional version of a Peano-like existence theorem. Two applications, one to a semilinear wave equation with delay and another one to a pseudoparabolic PDE in Mechanics, are included.
Citation
Ioan I. Vrabie. "A local existence theorem for a class of delay differential equations." Topol. Methods Nonlinear Anal. 48 (2) 597 - 612, 2016. https://doi.org/10.12775/TMNA.2016.023
Information