A Uniform Scheme for the Singularly Perturbed Riccati Equation.
A Uniformly Convergent Difference Scheme for a Semilinear Singular Perturbation Problem.
A uniformly convergent quadratic spline difference scheme for singular perturbation problems
A uniqueness result for ordinary differential equations with singular coefficients.
A useful proposition to nonlinear differential systems with a solution of the prescribed asymptotic properties
A variant of the complex Liouville-Green approximation theorem
We propose a variant of the classical Liouville-Green approximation theorem for linear complex differential equations of the second order. We obtain rigorous error bounds for the asymptotics at infinity, in the spirit of F. W. J. Olver’s formulation, by using rather arbitrary -progressive paths. This approach can provide higher flexibility in practical applications of the method.
A variant of the Smale's model for flocks formation.
A variational approach to homoclinic orbits in Hamiltonian systems.
A variational approach to implicit ODEs and differential inclusions
An alternative approach for the analysis and the numerical approximation of ODEs, using a variational framework, is presented. It is based on the natural and elementary idea of minimizing the residual of the differential equation measured in a usual Lp norm. Typical existence results for Cauchy problems can thus be recovered, and finer sets of assumptions for existence are made explicit. We treat, in particular, the cases of an explicit ODE and a differential inclusion. This approach also allows...
A variational formalism for the eigenvalues of fourth order boundary value problems.
A vector functional equation and linear differential equations.
A verified method for solving piecewise smooth initial value problems
In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview...
A version of non-Hamiltonian Liouville equation
In this paper we give a version of the theorem on local integral invariants of systems of ordinary differential equations. We give, as an immediate conclusion of this theorem, a condition which guarantees existence of an invariant measure of local dynamical systems. Results of this type lead to the Liouville equation and have been frequently proved under various assumptions. Our method of the proof is simpler and more direct.
A viability result for nonconvex semilinear functional differential inclusions
We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.
A viability result for second-order differential inclusions.
A viability result in the upper semicontinuous case.
A viable result for nonconvex differential inclusions with memory.
A view on differential inclusions.
A viral infection model with a nonlinear infection rate.
A Viterbo-Hofer-Zehnder type result for hamiltonian inclusions