Existence theorems for nonlinear functional differential equations of neutral type

Conditions are found upon satisfaction of which the differential equation

On two-point boundary value problems for systems of higher-order ordinary differential equations with singularities

The sufficient conditions of solvability and unique solvability of the two-point boundary value problems of Vallèe-Poussin and Cauchy-Niccoletti have been found for a system of ordinary differential equations of the form

An oscillation criterion for functional differential equations with deviating arguments

An oscillation criterion is given for the differential equation

Periodic boundary value problem of functional differential equations with perturbation

By coincidence degree, the existence of solution to the periodic boundary value problem of functional differential equations with perturbation     

Oscillation of forced neutral differential equations with positive and negative coefficients

In this paper the forced neutral difterential equation with positive and negative coefficients d/dt [x(t)-R(t)x(t-r)] P(t)x(t-x)-Q(t)x(t-σ)=f(t),t≥t0,is considered,where f∈L^1(t0,∞)交集C([t0,∞],R^ )and r,x,σ∈(0,∞),The sufficient conditions to oscillate for all solutions of this equation are studied.     

Unbounded solutions of differential equations of second order

In this paper, the existence of unbounded solutions for the following nonlinear asymmetric oscillator

Remarks on extremal solutions of differential equations with advanced argument

We show the existence of absolutely continuous extremal solutions to the problemx′(t)=f(t, x)h(t)))+g(t)),x(0)=x ₀, whereh is an arbitrary continuous deviated argument. Conditions for the uniqueness of solutions are given. Research partialy supported by grant UG BW 5100 - 5 - 0143 - 4     

Skorohod stochastic differential equations of diffusion type

Leta, b beC ²(R ¹)-functions with bounded derivatives of first and second order. We study stochastic differential equations

On a method to transform algebraic differential equations into universal equations

The paper introduces an algorithm which transforms homogeneous algebraic differential equations into universal differential equations (in the sense of L. A. Rubel) havingC ⁿ (ℝ)-solutions. By applications of the algorithm to different initial equations some new universal differential equations are found, and all the known equations due to R. J. Duffin are rediscovered with this method. Assuming weak conditions one can find Cⁿ(ℝ)-solutionsy of the differential equation close to any continuous function such that 1, with 0 ≤k ₁ <k ₂ < .... <k _s ≤n are linearly independent over the field of real algebraic numbers at the rational points q1,...,qs.     

A CRITERION OF THE NON-EXISTENCE OF PERIODIC SOLUTIONS FOR A GENERALIZED LI ENARD SYSTEM AND ITS APPLICATIONS

In this paper, a new criterion of the non-existence of periodic solutions for a generalized liénard system

Similarity solutions of differential equations for boundary layer approximations in porous media

This paper is concerned with the ordinary differential equation

Oscillations of certain second order nonlinear differential equations

A second order nonlinear differential equation

On solving implicit differential equations on parallel computers

We construct and analyse integration methods for solving initial value problems for implicit differential equations (IDEs) that can be efficiently used on parallel computer systems. We construct an IDE method for general IDEs of arbitrarily high index, and two methods that can be applied to partitioned IDEs. The partitioned IDE methods both exploit the special form of the problem and converge faster than the general IDE method. The first partitioned IDE method is suitable for higher-index problems, the second partitioned IDE method only applies to index 1 problems, but is considerably less expensive on parallel computers. This paper presents the results presented in June 1995 at the Seminario Matematico e Fisico organized by the Mathematics Department of the Polytechnics University of Milano. Conferenza tenuta da P.J. van der Houwen il 5 giugno 1995     

On the existence of periodic solutions of Rayleigh equations

In this paper, we study the existence of periodic solutions of Rayleigh equation

On the rapidly decreasing solutions for some systems of differential equations with unbounded coefficients

In this paper we continue the study of solvability of the non-homogeneous system of linear differential equations

A useful fixpoint theorem

A sufficient condition for each extensive mapping of an ordered set to have a fixpoint is presented. Financial support of the Grant Agency of the Czech Republic under the grant no. 201/93/0950 is gratefully acknowledged.     

Periodic orbits for a class of C 1 three-dimensional systems

We studyC ¹ perturbations of a reversible polynomial differential system of degree 4 in. We introduce the concept of strongly reversible vector field. If the perturbation is strongly reversible, the dynamics of the perturbed system does not change. For non-strongly reversible perturbations we prove the existence of an arbitrary number of symmetric periodic orbits. Additionally, we provide a polynomial vector field of degree 4 in with infinitely many limit cycles in a bounded domain if a generic assumption is satisfied. The first two authors are partially supported by a MCYT grant number MTM2005-06098-C02-01, and by a CICYT grant number 2005SGR 00550. The second author is partially supported by a FAPESP-BRAZIL grant 10246-2. All authors are also supported by the joint project CAPES-MECD grant HBP2003-0017.     

Stochastic invariant imbedding

We study stochastic differential equations of the type:

Asymptotically almost periodic solutions of abstract retarded functional differential equations of second order

We establish existence of asymptotically almost periodic mild solutions for a class of semi-linear second-order abstract retarded functional differential equations with infinite delay. Research supported in part by FONDECYT, grant 1050314.     

Operator splittings and spatial approximations for evolution equations

The convergence of various operator splitting procedures, such as the sequential, the Strang and the weighted splitting, is investigated in the presence of a spatial approximation. To this end the relevant notions and results of numerical analysis are presented, a variant of Chernoff’s product formula is proved and the general Trotter–Kato approximation theorem is used. The methods are applied to an abstract partial delay differential equation. To Rainer Nagel, our teacher and friend