A local existence theorem for a class of delay differential equations
KeywordsDelay differential equations, local existence, metric fixed point arguments, topological fixed point arguments, semilinear wave equation, pseudoparabolic equation
AbstractThe 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.
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