A General Cooperation Theorem for Hypercycles.
A general theorem concerning the growth of solutions of first-order algebraic differential equations
A geometric analysis of a singular ODE related to the study of a quasilinear PDE.
A gradient inequality at infinity for tame functions.
Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.
A Hille-Wintner comparison theorem for second order differential systems
A Leighton-Borůvka formula for Morse conjugate points
A linearization method in oscillation theory of half-linear second-order differential equations.
A Massera-type criterion for almost periodic solutions of higher-order delay or advance abstract functional differential equations.
A mean value property for pairs of integrals.
A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems.
A min-max theorem and its applications to nonconservative systems.
A modification and comparison of Filippov and Viktorovskij generalized solutions
A modification of the Sturm's theorem on separating zeros of solutions of a linear differential equation of the 2nd order
A modified van der Pol equation with delay in a description of the heart action
In this paper, a modified van der Pol equation is considered as a description of the heart action. This model has a number of interesting properties allowing reconstruction of phenomena observed in physiological experiments as well as in Holter electrocardiographic recordings. Our aim is to study periodic solutions of the modified van der Pol equation and take into consideration the influence of feedback and delay which occur in the normal heart action mode as well as in pathological modes. Usage...
A multiplicity result for periodic solutions to higher-order ordinary differential equations via the method of upper and lower solutions.
A Nearly-Periodic Boundary Value Problem for Second Order Differential Equations
A new look at an old comparison theorem
We present an integral comparison theorem which guarantees the global existence of a solution of the generalized Riccati equation on the given interval when it is known that certain majorant Riccati equation has a global solution on .
A new oscillation criterion for forced second-order quasilinear differential equations.
A new proof of multisummability of formal solutions of non linear meromorphic differential equations
We give a new proof of multisummability of formal power series solutions of a non linear meromorphic differential equation. We use the recent Malgrange-Ramis definition of multisummability. The first proof of the main result is due to B. Braaksma. Our method of proof is very different: Braaksma used Écalle definition of multisummability and Laplace transform. Starting from a preliminary normal form of the differential equationthe idea of our proof is to interpret a formal power series solution...
A nonlinear periodic system with nonsmooth potential of indefinite sign
In this paper we consider a nonlinear periodic system driven by the vector ordinary -Laplacian and having a nonsmooth locally Lipschitz potential, which is positively homogeneous. Using a variational approach which exploits the homogeneity of the potential, we establish the existence of a nonconstant solution.