Radial solutions of equations and inequalities involving the -Laplacian.
Ranges of -homogeneous operators and their perturbations
Rank-2 distributions satisfying the Goursat condition : all their local models in dimension 7 and 8
Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8
We study the rank–2 distributions satisfying so-called Goursat condition (GC); that is to say, codimension–2 differential systems forming with their derived systems a flag. Firstly, we restate in a clear way the main result of[7] giving preliminary local forms of such systems. Secondly – and this is the main part of the paper – in dimension 7 and 8 we explain which constants in those local forms can be made 0, normalizing the remaining ones to 1. All constructed equivalences are explicit. ...
Rayleigh principle for linear Hamiltonian systems without controllability∗
In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools...
Rayleigh principle for linear Hamiltonian systems without controllability∗
In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools...
Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems
Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.
Rearrangements of the coefficients of ordinary differential equations.
Recent applications of the theory of Lie systems in Ermakov systems.
Recent existence results for second-order singular periodic differential equations.
Recent results concerning dynamic equations on time scales.
Reconstruction of map projection, its inverse and re-projection
This paper focuses on the automatic recognition of map projection, its inverse and re-projection. Our analysis leads to the unconstrained optimization solved by the hybrid BFGS nonlinear least squares technique. The objective function is represented by the squared sum of the residuals. For the map re-projection the partial differential equations of the inverse transformation are derived. They can be applied to any map projection. Illustrative examples of the stereographic and globular Nicolosi projections...
Reducibility and point spectrum for linear quasi-periodic skew-products.
Reducibility of zero curvature equations.
Reductibilite d'un systeme differentiel lineaire (Reductibility of a Linear Differential System)
Reduction of differentiable equations with impulse effect.
Regular half-linear second order differential equations
We introduce the concept of the regular (nonoscillatory) half-linear second order differential equation and we show that if (*) is regular, a solution of this equation such that for large is principal if and only if Conditions on the functions are given which guarantee that (*) is regular.
Regularity, nonoscillation and asymptotic behaviour of solutions of second order linear equations.
Regularized traces and conditions of smooth periodicity for the potential of Sturm-Liouville equation.
Regularly Varying Solutions of Perturbed Euler Differential Equations and Related Functional Differential Equations