Geodesic
Existence and uniqueness of solutions for quasi-linear differential equations with deviating arguments
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We prove the existence and uniqueness of a local solution to a quasi-linear differential equation of parabolic type with deviated argument in an arbitrary Banach space. The results are obtained by applying the Sobolevskii-Tanabe theory of parabolic equations, fractional powers of operators, and the Banach fixed point theorem. We include an example that illustrates the theory.
Classification : 34G20, 34K30, 35K90, 47N20
Keywords: analytic semigroup, parabolic equation, deviated argument, Banach fixed point theorem 
@article{EJDE_2012__2012__a10,
     author = {Haloi, Rajib and Bahuguna, Dhirendra and Pandey, Dwijendra N.},
     title = {Existence and uniqueness of solutions for quasi-linear differential equations with deviating arguments},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a10/}
}
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Haloi, Rajib; Bahuguna, Dhirendra; Pandey, Dwijendra N. Existence and uniqueness of solutions for quasi-linear differential equations with deviating arguments. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a10/