We prove, in this paper, local existence and uniqueness of solution for the frictional Newton-Schrödinger equation in three dimensions. Further we show that the blow-up alternative holds true as well as the continuous dependence of the solution w.r.t. the initial data. Our method is rather direct and based essentially on a fixed point-type theorem due to Weissinger and an approximation process.

In this paper, we deal with a transmission problem for a class of quasilinear pseudoparabolic equations. Existence, uniqueness and continuous dependence of the solution upon the data are obtained via the Rothe method. Moreover, the convergence of the method and an error estimate of the approximations are established.

This paper deals with an identification problem for degenerate parabolic equations. The problem consists of recovering a source term from the knowledge of an additional observation of the solution by exploiting some accessible measurements. Existence, uniqueness and continuous dependence results are proved for the problem. Applications to the source identification problems for the Poissonheat e...

General delay dynamical systems in which uncertainty is present in the form of probability measure dependent dynamics are considered. Several motivating examples arising in biology are discussed. A functional analytic framework for investigating well-posedness (existence, uniqueness and continuous dependence of solutions), inverse problems, sensitivity analysis and approximations of the measure...

A logistic matrix model for age-structured population dynamics is constructed. This model discretizes a continuous, density-dependent model with age structure, i.e. it is an extension of the logistic model to the case of age-dependence. We prove the existence and uniqueness of its equilibrium and give a necessary and sufficient condition for the local stability of the equilibrium.

this paper develops an analysis of budget deficit financing in termsof a crowding out or crowding in effect on the activity of the privatesector for the economies of iran and algeria as two mena countries,(because of its economic structures (dependence on oil revenue)) duringthe period 1970-2012 by using cointegration and vector errorcorrection approaches. the analysis confirms the existence of...

We prove the existence, uniqueness, and the continuous dependence of a generalized solution upon the data of certain parabolic and hyperbolic equations with a boundary integral condition. The proof uses a functional analysis method based on a priori estimates established in nonclassical function spaces and on the density of the range of the linear operator associated to the abstract formulation...

In this paper, we study rotation numbers of random dynamical systems on the circle. We prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems. As an application, we prove a theorem on analytic conjugacy to a circle rotation.

In the present paper, we investigate the existence, uniqueness and continuous dependence on initial data of mild solutions of first order nonlocal semilinear functional impulsive integro-differential equations of more general type with finite delay in Banach spaces. Our analysis is based on semigroup theory and Banach contraction theorem.

In the paper the existence and continuous dependence of a kind of minimax solution to the dual Hamilton-Jacobi equations is proved. The main difficulties which appear here are a special type of the boundary conditions and the transversality conditions which that solution must satisfy. That type of problems come from optimal control and game theory.