Asymptotic solutions of forced nonlinear second order differential equations and their extensions.
Asymptotic stability of the extended Tjon-Wu model.
Asymptotics of a solution of a nonlinear system of diffusion of a magnetic field into a substance.
Asymptotics of integrodifferential models with integrable kernels II.
Bifurcation theory of the time-dependent von Kármán equations
In this paper the author studies existence and bifurcation of a nonlinear homogeneous Volterra integral equation, which is derived as the first approximation for the solution of the time dependent generalization of the von Kármán equations. The last system serves as a model for stability (instability) of a thin rectangular visco-elastic plate whose two opposite edges are subjected to a constant loading which depends on the parameters of proportionality of this boundary loading.
Biorthogonal systems approximating the solution of the nonlinear Volterra integro-differential equation.
Block-by-block method for solving nonlinear Volterra-Fredholm integral equation.
Boyd index and nonlinear Volterra equations.
In mathematical models of some physical phenomena a new class of nonlinear Volterra equations appears ([5],[6]). The equations belonging to this class have u = 0 as a solution (trivial solution), but with respect to their physical meaning, nonnegative nontrivial solutions are of prime importance.
Branch points of algebraic integral equations
Closed-form solution of a singular nonlinear integral equation
Continuity, compactness, fixed points, and integral equations.
Continuous dependence for semilinear parabolic functional equations without uniqueness
Controllability of Infinite Rime Horizon of Neutral Functional Differential and Integrodifferential Inclusions in Banach Spaces
Convergence Analysis of Discretization Methods for Nonlinear First Kind Volterra Integral Equations.
Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type
In this paper, we deal with a system of integral algebraic equations of the Hessenberg type. Using a new index definition, the existence and uniqueness of a solution to this system are studied. The well-known piecewise continuous collocation methods are used to solve this system numerically, and the convergence properties of the perturbed piecewise continuous collocation methods are investigated to obtain the order of convergence for the given numerical methods. Finally, some numerical experiments...
Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions
We provide a semilocal convergence analysis for Newton-type methods using our idea of recurrent functions in a Banach space setting. We use Zabrejko-Zinčenko conditions. In particular, we show that the convergence domains given before can be extended under the same computational cost. Numerical examples are also provided to show that we can solve equations in cases not covered before.
Convex solutions of a nonlinear integral equation of Urysohn type.
Corrections to the article `Weighted Monte Carlo methods for approximate solution of a nonlinear Boltzmann equation'.
Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation
In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius in