Monotone trajectories of dynamical systems and Clarke's generalized Jacobian.
Monotonic properties of zeros and extremants of the differential equation
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...
Monotonicity of the period map of a non-Hamiltonian center.
Monotonicity properties of oscillatory solutions of differential equation
We obtain monotonicity results concerning the oscillatory solutions of the differential equation . The obtained results generalize the results given by the first author in [1] (1976). We also give some results concerning a special case of the above differential equation.
Monotonicity properties of the linear combination of derivatives of some special functions
Monotonicity theorems concerning differential equations
Monotonicity theorems for second order non-linear differential equations
More on oscillation of th-order equations.
Morse theory and existence of periodic solutions of convex hamiltonian systems
Motion of spirals by crystalline curvature
Motion of spirals by crystalline curvature
Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
Multibump solutions for a class of lagrangian systems slowly oscillating at infinity
Multibump solutions for an almost periodically forced singular Hamiltonian system.
Multichain-type solutions for Hamiltonian systems.
Multi-dimensional Cartan prolongation and special k-flags
Since the mid-nineties it has gradually become understood that the Cartan prolongation of rank 2 distributions is a key operation leading locally, when applied many times, to all so-called Goursat distributions. That is those, whose derived flag of consecutive Lie squares is a 1-flag (growing in ranks always by 1). We first observe that successive generalized Cartan prolongations (gCp) of rank k + 1 distributions lead locally to all special k-flags: rank k + 1 distributions D with the derived...
Multi-parameter symmetries of first order ordinary differential equations.
Multiple global bifurcation branches for nonlinear Picard problems.
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.