Geodesic
Existence and uniqueness of solutions for quasi-linear differential equations with deviating arguments
Electronic journal of differential equations, Tome 2012 (2012)
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},
     year = {2012},
     volume = {2012},
     zbl = {1242.34109},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a10/}
}
TY  - JOUR
AU  - Haloi,  Rajib
AU  - Bahuguna,  Dhirendra
AU  - Pandey,  Dwijendra N.
TI  - Existence and uniqueness of solutions for quasi-linear differential equations with deviating arguments
JO  - Electronic journal of differential equations
PY  - 2012
VL  - 2012
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LA  - en
ID  - EJDE_2012__2012__a10
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%A Bahuguna,  Dhirendra
%A Pandey,  Dwijendra N.
%T Existence and uniqueness of solutions for quasi-linear differential equations with deviating arguments
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a10/
%G en
%F EJDE_2012__2012__a10
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/