Monotonicity theorems concerning differential equations
Monotonicity theorems for second order non-linear differential equations
Morales-Ramis Theorems via Malgrange pseudogroup
In this article we give an obstruction to integrability by quadratures of an ordinary differential equation on the differential Galois group of variational equations of any order along a particular solution. In Hamiltonian situation the condition on the Galois group gives Morales-Ramis-Simó theorem. The main tools used are Malgrange pseudogroup of a vector field and Artin approximation theorem.
More on oscillation of th-order equations.
Morse theory and existence of periodic solutions of convex hamiltonian systems
Morse-Sard theorem in infinite dimensional Banach spaces and investigation of the set of all critical levels
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.
Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion
We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never...
Motion with friction of a heavy particle on a manifold - applications to optimization
Let Φ : H → R be a C2 function on a real Hilbert space and ∑ ⊂ H x R the manifold defined by ∑ := Graph (Φ). We study the motion of a material point with unit mass, subjected to stay on Σ and which moves under the action of the gravity force (characterized by g>0), the reaction force and the friction force ( is the friction parameter). For any initial conditions at time t=0, we prove the existence of a trajectory x(.) defined on R+. We are then interested in the asymptotic behaviour of...
Motion with friction of a heavy particle on a manifold. Applications to optimization
Let be a function on a real Hilbert space and the manifold defined by Graph . We study the motion of a material point with unit mass, subjected to stay on and which moves under the action of the gravity force (characterized by ), the reaction force and the friction force ( is the friction parameter). For any initial conditions at time , we prove the existence of a trajectory defined on . We are then interested in the asymptotic behaviour of the trajectories when . More precisely,...
Mouvement à un nombre fini de degrés de liberté avec contraintes unilatérales : cas avec perte d'énergie
m-Point Boundary Value Problems
m-Reduction of ordinary differential equations
Multi Point Boundary Value Problems for Second Order Differential Inclusions
Multi point boundary-value problems at resonance for n-order differential equations: Positive and monotone solutions.
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...