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Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non dense domain. (English) Zbl 0985.34052
Existence and uniqueness of so-called pseudo-almost periodic solutions to the abstract semilinear evolution equation $x'(t)= Ax(t)+ f(t, x(t)),\qquad t\in\mathbb{R},$ is proved, where $$A$$ is a linear unbounded (not necessarily dense defined) operator in some Banach space that generates a continuous semigroup. Moreover, $$f$$ is some continuous mapping that is pseudo-almost periodic in $$t$$ and Lipschitzian with respect to the second argument.
The results can be applied to delay and partial differential equations as it is done by the authors in two examples for a semilinear first-order partial differential equation.

##### MSC:
 34G20 Nonlinear differential equations in abstract spaces 34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations 35K55 Nonlinear parabolic equations
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##### References:
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