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Abstract. In this paper we present some results relative to existence, uniqueness, integral inequalities and data dependence for the solutions of the functional Volterra-Fredholm integral equation with deviating argument in a Banach space: ,y,s,t,u(s,t))dsdt, x,y ∈ R + by Picard operators technique.

In this paper we investigate the Ulam-Hyers-Rassias stability for some quasilinear partial differential equations.

The aim of this paper is to give some types of Ulam stability for a pseudoparabolic partial differential equation. In this case we consider Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability. We investigate some new applications of the Gronwall lemmas to the Ulam stability of a nonlinear pseudoparabolic partial differential equations.

The aim of this paper is to investigate generalized Ulam–Hyers stability and generalized Ulam–Hyers–Rassias stability for a system of partial differential equations of first order. More precisely, we consider a system of two nonlinear equations of first order with an unknown function of two independent variables, which satisfy the corresponding compatibility condition. The study method is that of differential inequalities of the Gronwall type.