| This work is devoted to the study of a class of higher order Kadomtsev-Petviashvili-Burgers (KPB) equations, followed by that of nonlocal Cauchy problems in Banach spaces, and of a first order semilinear Volterra equation.; The investigation was carried out by using monotonicity methods, Leray-Schauder type techniques, fixed point theorems, methods and results for differential equations governed by m-accretive operators in Banach spaces, and Fourier analysis.; The main contributions of our study are the following. First we establish the existence, uniqueness, and continuous dependence on data of anti-periodic traveling wave solutions to a class of KPB equations. We then obtain existence, uniqueness, regularity, continuous dependence, and asymptotic results for a non-local Cauchy problem associated to an abstract functional differential equation. Finally, we prove the existence of periodic solutions to a semilinear Volterra integrodifferential equation in a Hilbert space. |
