A second-order impulsive Cauchy problem.
A second-order nonlinear problem with two-point and integral boundary conditions.
A Series Method for Solving Nonlinear Two-Point Boundary Value Problems.
A simple boundedness theorem for a Liénard equation with damping
A simple complement to Miklusiński's operational calculus
A simple mathematical model of the human liver
The parameter estimation problem for a continuous dynamical system is a difficult one. In this paper we study a simple mathematical model of the liver. For the parameter identification we use the observed clinical data obtained by the BSP test. Bellman’s quasilinearization method and its modifications are applied.
A simple method for constructing non-liouvillian first integrals of autonomous planar systems
We show that a transformation method relating planar first-order differential systems to second order equations is an effective tool for finding non-liouvillian first integrals. We obtain explicit first integrals for a subclass of Kukles systems, including fourth and fifth order systems, and for generalized Liénard-type systems.
A simple model of thermoelectric oscillations
A system of ordinary differential equations modelling an electric circuit with a thermistor is considered. Qualitative properties of solution are studied, in particular, the existence and nonexistence of time-periodic solutions (the Hopf bifurcation).
A simple proof of a semi-Fredholm principle for periodically forced systems with homogeneous nonlinearities
A simple proof of the non-integrability of the first and the second Painlevé equations
The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.
A simple proof of the spectral continuity of the Sturm-Liouville problem
The aim of this article is to present a simple proof of the theorem about perturbation of the Sturm-Liouville operator in Liouville normal form.
A singular boundary value problem for neutral equations.
A singular eigenvalue problem for second order linear ordinary differential equations.
A singular functional-differential equation.
A singular initial value problem for second and third order differential equations
A singular initial value problem for some functional differential equations.
A singular initial value problem for the equation
We consider the problem of the existence of positive solutions u to the problem , (g ≥ 0,x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.
A singular nonlinear boundary-value problem.
A singular ODE related to quasilinear elliptic equations.
A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.
Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle...