A high accuracy method for solving ODEs with continuous right-hand side.
A higher-order method for nonlinear singular two-point boundary value problems.
A Hille-Wintner comparison theorem for second order differential systems
A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations.
A KAM phenomenon for singular holomorphic vector fields
Let X be a germ of holomorphic vector field at the origin of Cn and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are biholomorphic to the intersection...
A KAM-theorem for some nonlinear partial differential equations
A Kneser-type theorem for the equation in locally convex spaces.
A Laplace decomposition algorithm applied to a class of nonlinear differential equations.
A Lax formalism for the elliptic difference Painlevé equation.
A Leighton-Borůvka formula for Morse conjugate points
A limit set trichotomy for order-preserving systems on time scales.
A Limit-Point Criterion for Separated Dirac Operators and a Little Known Result on Riccati's Equation.
A linear condition determining local or global existence for nonlinear problems
Given a nonlinear autonomous system of ordinary or partial differential equations that has at least local existence and uniqueness, we offer a linear condition which is necessary and sufficient for existence to be global. This paper is largely concerned with numerically testing this condition. For larger systems, principals of computations are clear but actual implementation poses considerable challenges. We give examples for smaller systems and discuss challenges related to larger systems. This...
A linear functional differential equation with distributions in the input.
A linear inequality of Gronwall's type containing multiple integral
A linearization method in oscillation theory of half-linear second-order differential equations.
A Lyapunov function for pullback attractors of nonautonomous differential equations.
A Massera type criterion for a partial neutral functional differential equation.
A Massera-type criterion for almost periodic solutions of higher-order delay or advance abstract functional differential equations.
A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation
In the present paper, a mathematical model, originally proposed by Danziger and Elmergreen and describing the thyroid-pituitary homeostatic mechanism, is modified and analyzed for its physiological and clinical significance. The influence of different system parameters on the stability behavior of the system is discussed. The transportation delays of different hormones in the bloodstream, both in the discrete and distributed forms, are considered. Delayed models are analyzed regarding the stability...