A barrier method for quasilinear ordinary differential equations of the curvature type
A class of generalized uniform asymptotic expansions.
A classical approach to eigenvalue problems associated with a pair of mixed regular Sturm-Liouville equations. I.
A continuation method for motion-planning problems
We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...
A continuation method for motion-planning problems
We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...
A derivative array approach for linear second order differential-algebraic systems.
A differentiable dependence on the right-hand side of solutions of ordinary differential equations
A finite element method for a two point boundary value problem with a small parameter affecting the highest derivative
A model for gene activation.
A modified regularization method.
A monotone iterative method for boundary value problems of parametric differential equations.
A new method of proof of Filippov’s theorem based on the viability theorem
Filippov’s theorem implies that, given an absolutely continuous function y: [t 0; T] → ℝd and a set-valued map F(t, x) measurable in t and l(t)-Lipschitz in x, for any initial condition x 0, there exists a solution x(·) to the differential inclusion x′(t) ∈ F(t, x(t)) starting from x 0 at the time t 0 and satisfying the estimation where the function γ(·) is the estimation of dist(y′(t), F(t, y(t))) ≤ γ(t). Setting P(t) = x ∈ ℝn: |x −y(t)| ≤ r(t), we may formulate the conclusion in Filippov’s theorem...
A non-linear hyperbolic equation.
A note on boundary value problems for second order differential equations
A note on existence theorem of Peano
An ODE with non-Lipschitz right hand side has been considered. A family of solutions with -dependence of the initial data has been obtained. A special set of initial data has been constructed. In this set the family is continuous. The measure of this set has been estimated.
A note on the criteria of uniqueness of the solution of equation
A note on the differential equation
A note on uniqueness of Cauchy problems associated to planar Hamiltonian systems.
A Picard method without Lipschitz continuity for some ordinary differential equations
A remark on uniqueness criteria for initial value problem