Displaying similar documents to “Existence of Solutions of Abstract Nonlinear Mixed Functional Integrodifferential equation with nonlocal conditions”

Some Nonlinear Evolution Problems in Mixed Form

Ulisse Stefanelli, Augusto Visintin (2009)

Bollettino dell'Unione Matematica Italiana

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This work deals with some abstract equations, either linear or nonlinear, arising from the so-called mixed formulation of PDEs of elliptic and parabolic type. This class of variational formulations turns out to be particularly relevant in connection with the development of finite elements approximations. We prove the well-posedness of both the stationary and the evolution problems.

Infinite systems of first order PFDEs with mixed conditions

W. Czernous (2008)

Annales Polonici Mathematici

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We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral...

Numerical method for the mixed Volterra-Fredholm integral equations using hybrid Legendre functions

Nemati, S., Lima, P., Ordokhani, Y.

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A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise polynomial approximation, for the space discretization. We extend the method to nonlinear mixed Volterra-Fredholm integral equations. Finally, the method is tested on a number of problems and numerical results are given.

Existence results for systems with nonlinear coupled nonlocal initial conditions

Octavia Bolojan, Gennaro Infante, Radu Precup (2015)

Mathematica Bohemica

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The purpose of the present paper is to study the existence of solutions to initial value problems for nonlinear first order differential systems subject to nonlinear nonlocal initial conditions of functional type. The approach uses vector-valued metrics and matrices convergent to zero. Two existence results are given by means of Schauder and Leray-Schauder fixed point principles and the existence and uniqueness of the solution is obtained via a fixed point theorem due to Perov. Two examples...