Monotone iterative method for semilinear impulsive evolution equations of mixed type in Banach spaces.
Monotone methods applied to some higher order boundary value problems.
Monotone technique for second order discontinuous differential inclusions.
Monotone trajectories of differential inclusions in Banach spaces.
Monotonic properties of zeros and extremants of the differential equation
Monotonicity and Boundedness in Implicit Runge-Kutta Methods.
Monotonicity and differential properties of the value functions in optimal control.
Monotonicity of the number of passages in linear chains and of the basis reproduction number in epidemic models.
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.
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-Reduction of ordinary differential equations
Multi Point Boundary Value Problems for Second Order Differential Inclusions
Multi-parameter symmetries of first order ordinary differential equations.
Multiple positive solutions for -type semipositone conjugate boundary value problems of nonlinear fractional differential equations.