Geodesic
Existence results for a class of semi-linear evolution equations
Electronic journal of differential equations, Tome 2001 (2001)
We prove the existence of regular solutions for the quasi-linear evolution

$ {d \over dt}(x(t)+g(t,x(t))=Ax(t)+f(t,x(t)), $

where $A$ is the infinitesimal generator of an analytic semigroup of bounded linear operators defined on a Banach space and the functions $f, g$ are continuous.
Classification : 35A05, 34G20, 34A09
Keywords: Banach spaces, semigroup of linear operators, abstract differential equations, fractional powers of closed operators, regular solutions 
@article{EJDE_2001__2001__a164,
     author = {Hern\'andez M.,  Eduardo},
     title = {Existence results for a class of semi-linear evolution equations},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0973.35009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a164/}
}
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JO  - Electronic journal of differential equations
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Hernández M.,  Eduardo. Existence results for a class of semi-linear evolution equations. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a164/