Existence of solutions for non-linear systems of differential-functional equations of parabolic type in an arbitrary domain

S. Brzychczy

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Displaying similar documents to “Existence of solutions for non-linear systems of differential-functional equations of parabolic type in an arbitrary domain”

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This paper is concerned with iterative methods for parabolic functional differential equations with initial boundary conditions. Monotone iterative methods are discussed. We prove a theorem on the existence of solutions for a parabolic problem whose right-hand side admits a Jordan type decomposition with respect to the function variable. It is shown that there exist Newton sequences which converge to the solution of the initial problem. Differential equations with deviated variables...

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Monotone iteration for infinite systems of parabolic equations with functional dependence

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Existence of solutions with exponential growth for nonlinear differential-functional parabolic equations

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We consider the Cauchy problem for nonlinear parabolic equations with functional dependence. We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.

On a linear functional equation with a mean-type mapping having no fixed points

Katarzyna Sajbura (2005)

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Our aim is to study continuous solutions φ of the classical linear iterative equation φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y), where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.

Existence and uniqueness of solutions of nonlinear infinite systems of parabolic differential-functional equations

Stanisław Brzychczy (2001)

Annales Polonici Mathematici

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We consider the Fourier first initial-boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations of parabolic type. The right-hand sides of the system are functionals of unknown functions. The existence and uniqueness of the solution are proved by the Banach fixed point theorem.