Existence of solutions for an abstract second-order differential equation with nonlocal conditions.
Existence of solutions for discontinuous functional equations and elliptic boundary-value problems.
Existence of solutions for infinite systems of parabolic equations with functional dependence
The Cauchy problem for an infinite system of parabolic type equations is studied. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. We prove the existence and uniqueness of a bounded solution under Carathéodory type conditions and its differentiability, as well as the existence and uniqueness in the class of functions satisfying a natural growth condition. Both results are obtained by the fixed point method.
Existence of solutions for non-linear systems of differential-functional equations of parabolic type in an arbitrary domain
Existence of solutions of the Cauchy problem for semilinear infinite systems of parabolic differential-functional equations.
Existence of solutions to generalized von Foerster equations with functional dependence
We prove the existence of solutions to a differential-functional system which describes a wide class of multi-component populations dependent on their past time and state densities and on their total size. Using two different types of the Hale operator, we incorporate in this model classical von Foerster-type equations as well as delays (past time dependence) and integrals (e.g. influence of a group of species).
Existence of solutions to nonlinear parabolic problems with delay.
Existence of solutions with exponential growth for nonlinear differential-functional parabolic equations
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.
Existence of time periodic solutions for one-dimensional Newtonian filtration equation with multiple delays.
Existence results for abstract partial neutral integro-differential equation with unbounded delay.
Existence results for first order impulsive semilinear evolution inclusions.
Existence results for impulsive evolution differential equations with state-dependent delay.
Existence results for impulsive semilinear damped differential inclusions.
Existence results on the semiinfinite interval for first and second order integrodifferential equations in Banach spaces with nonlocal conditions
Existence, uniqueness and continuous dependence for a hereditary nonlinear functional partial differential equation of the first order
Explicit difference schemes for nonlinear differential functional parabolic equations with time dependent coefficients-convergence analysis
We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.
Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping.
First order partial functional differential equations with unbounded delay.
Forced oscillation of certain hyperbolic equations with continuous distributed deviating arguments
Certain hyperbolic equations with continuous distributed deviating arguments are studied, and sufficient conditions are obtained for every solution of some boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multi-dimensional oscillation problems to one-dimensional oscillation problems for functional differential inequalities by using some integral means of solutions.
Forced oscillations of a class of nonlinear delay hyperbolic equations