An asymptotic formula for solutions of nonoscillatory half-linear differential equations
We establish a Hartman type asymptotic formula for nonoscillatory solutions of the half-linear second order differential equation
An elliptic problem with arbitrarily small positive solutions.
An epidemiological model of Rift Valley fever.
An equation with no -periodic solutions.
An equivalence theorem concerning population growth in a variable environment.
An existence result on periodic solutions of an ordinary -Laplacian system.
An existence theorem for bounded solutions of differential equations in Banach spaces
An existence theorem for periodic boundary value problems for systems of second order diffferential equations
An exotic flow on a compact surface
In 1988 Anosov [1] published the construction of an example of a flow (continuous real action) on a cylinder or annulus with a phase portrait strikingly different from our normal experience. It contains orbits whose -limit sets contain a non-periodic orbit along with a simple closed curve of fixed points, but these orbits do not wrap down on this simple closed curve in the usual way. In this paper we modify some of Anosov’s methods to construct a flow on a surface of genus with equally striking...
An extension of Milloux's theorem to half-linear differential equations.
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 index for periodic orbits of functional differential equations.
An inertial manifold and the principle of spatial averaging.
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 for perturbed nonlinear functional differential equations, with applications to periodic solutions and nonlinear boundary value problems.
An invariant manifold of slowly oscillating solutions for x(t) = - ...x(t) + f(x(t-1)).