Abstract
A recent nonlinear alternative for contraction maps in Frechet spaces due to Frigon and Granas (Resultats de type Leray-Schauder pour des contractions sur des espaces de Frechet, Ann. Sci. Math. Quebec22, (2), 161–168 (1998)), combined with semigroup theory, is used to investigate the existence and uniqueness of mild solutions for first-and second-order functional semi linear and neutral damped differential equations in Frechet space.
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