An illustrative example for the Perron condition
An Improved Boundary Layer Estimate for a Singularly Perturbed Initial Value Problem.
An improved existence and uniqueness criterion for periodic solutions of a Duffing type p-Laplacian equation.
An improved oscillation theorem for nonlinear differential equations of advanced type
This paper deals with the oscillatory solutions of the first order nonlinear advanced differential equation. The aim of the present paper is to obtain an oscillation condition for this equation. This result is new and improves and correlates many of the well-known oscillation criteria that were in the literature. Finally, an example is given to illustrate the main result.
An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system
In this paper, an improvement of the global region for the non-existence of limit cycles of the Bogdanov-Takens system, which is well-known in the Bifurcation Theory, is given by two ideas. The first is to apply the existence of the algebraic invariant curve of the system to the Bendixson-Dulac criterion, and the second is to consider a necessary condition in order that a closed orbit of the system includes two equilibrium points. In virtue of these methods, it shall be shown that our previous result...
An impulsive nonlinear singular version of the Gronwall-Bihari inequality.
An impulsive two-prey one-predator system with seasonal effects.
An indefinite eigenvalue problem with eigenparameter in the two boundary conditions.
An index for periodic orbits of functional differential equations.
An inertial manifold and the principle of spatial averaging.
An initial value problem for a functiona equation.
An initial value problem fora third order differential equation
For an initial value problem u'''(x) = g(u(x)), u(0) = u'(0) = u''(0) = 0, x > 0, some theorems on existence and uniqueness of solutions are established.
An instability theorem for a certain vector differential equation of fourth order.
An integral condition of oscillation for equation with nonnegative coefficients
Our aim in this paper is to obtain a new oscillation criterion for equation with a nonnegative coefficients which extends and improves some oscillation criteria for this equation. In the special case of equation (*), namely, for equation , our results solve the open question of .
An integral equation associated with linear homogeneous differential equations.
An integral equation for perturbed nonlinear functional differential equations, with applications to periodic solutions and nonlinear boundary value problems.
An interplay between the weak form of Peano's theorem and structural aspects of Banach spaces
We establish some results that concern the Cauchy-Peano problem in Banach spaces. We first prove that a Banach space contains a nontrivial separable quotient iff its dual admits a weak*-transfinite Schauder frame. We then use this to recover some previous results on quotient spaces. In particular, by applying a recent result of Hájek-Johanis, we find a new perspective for proving the failure of the weak form of Peano's theorem in general Banach spaces. Next, we study a kind of algebraic genericity...
An Intracellular Delay-Differential Equation Model of the HIV Infection and Immune Control
Previous work has shown that intracellular delay needs to be taken into account to accurately determine the half-life of free virus from drug perturbation experiments [1]. The delay also effects the estimated value for the infected T-cell loss rate when we assume that the drug is not completely effective [19]. Models of virus infection that include intracellular delay are more accurate representations of the biological data. We analyze a non-linear model of the human immunodeficiency virus (HIV)...
An Invariance Problem for Control Systems with Deterministic Uncertainty
This paper deals with a class of nonlinear control systems in in presence of deterministic uncertainty. The uncertainty is modelled by a multivalued map F with nonempty, closed, convex values. Given a nonempty closed set from a suitable class, which includes the convex sets, we solve the problem of finding a state feedback ū(t,x) in such a way that K is invariant under any system dynamics f. As a system dynamics we consider any continuous selection of the uncertain controlled dynamics F.
An invariant manifold of slowly oscillating solutions for x(t) = - ...x(t) + f(x(t-1)).