L'existence d'une solution périodique d'une équation différentielle dans le cas où le second membre de l'équation n'est pas monotone par rapport à x
Limit cycles in a Kolmogorov-type model.
Limit properties of solutions of singular second-order differential equations.
Linking method for periodic non-autonomous fourth-order differential equations with superquadratic potentials.
Ljusternik-Schnirelman theory with local Palais-Smale condition and singular dynamical systems
Local method of nonlinear analysis
Localization of periodic orbits of autonomous systems based on high-order extremum conditions.
Mathematical theory of the bufferness phenomenon in oscillatory systems with distributed parameters.
Maximum Principles for Linear Difference-Differential Opeartors in Periodic Function Spaces.
Modeling the role of constant and time varying recycling delay on an ecological food chain
We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the...
Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions
The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.
Monotone Methods for Periodic solutions of Second Order Scalar Functional Differential Equations.
Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems
We first examine conditions implying monotonicity of the period function for potential systems with a center at 0 (in the whole period annulus). We also present a short comparative survey of the different criteria. We apply these results to quadratic Loud systems for various values of the parameters D and F. In the case of noncritical periods we propose an algorithm to test the monotonicity of the period function for . Our results may be viewed as a contribution to proving (or disproving) a conjecture...
Monotonicity of the period function for some planar differential systems. Part II: Liénard and related systems
We are interested in conditions under which the two-dimensional autonomous system ẋ = y, ẏ = -g(x) - f(x)y, has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function...
Morse theory and existence of periodic solutions of convex hamiltonian systems
Multiple periodic solutions for Hamiltonian systems with singular potential
In this Note we prove the existence of infinitely many periodic solutions of prescribed period for a Hamiltonian system with a singular potential.
Multiple periodic solutions of some forced hamiltonian systems and the generalized saddle point theorem.
Multiple periodic solutions to a suspension bridge O. D. E.
Multiple positive periodic solutions to a non-autonomous Lotka-Volterra predator-prey system with harvesting terms.
Multiple positive solutions of a nonlinear fourth order periodic boundary value problem
The fourth order periodic boundary value problem , 0 < t < 2π, with , i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of .