EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR QUASI-LINEAR DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

Rajib Haloi, Dhirendra Bahuguna, Dwijendra Pandey
2012 Electronic Journal of Differential Equations   unpublished
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 Sobolevski ˘ i-Tanabe theory of parabolic equations, fractional powers of operators , and the Banach fixed point theorem. We include an example that illustrates the theory.
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