On the two-point boundary value problem for quadratic second-order differential equations and inclusions on manifolds.
On the two-point boundary-value problem for the Riccati matrix differential equation
Constructive sufficient conditions for univalent resolvability of a two-point boundary value problem for nonlinear Riccati equation are obtained. An illustrative example is given.
On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations
The two-point boundary value problem is considered, where , and for . The existence of positive solutions is well-known. Several sufficient conditions have been obtained for the uniqueness of positive solutions. On the other hand, a non-uniqueness example was given by Moore and Nehari in 1959. In this paper, new uniqueness results are presented.
On the worst scenario method: a modified convergence theorem and its application to an uncertain differential equation
We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient.
On the worst scenario method: Application to uncertain nonlinear differential equations with numerical examples
On two-point boundary value problems for systems of higher-order ordinary differential equations with singularities.
On two-point boundary value problems for systems of ordinary non-linear, first-order differential equations
On two-points boundary value problems for ordinary nonlinear differential equations of the fourth order in the Colombeau algebra
On uniqueness conditions for decreasing solutions of semilinear elliptic equations.
On Urabe's application of Newton's method to nonlinear boundary value problems
On vector boundary value problems without growth restrictions.
One-dimensional elliptic equation with concave and convex nonlinearities.
One-step methods for ordinary differential equations with parameters
In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given.
One-step methods for two-point boundary value problems in ordinary differential equations with parameters
A general theory of one-step methods for two-point boundary value problems with parameters is developed. On nonuniform nets , one-step schemes are considered. Sufficient conditions for convergence and error estimates are given. Linear or quadratic convergence is obtained by Theorem 1 or 2, respectively.
Operator type expansion-compression fixed point theorem.
Opposing flows in a one dimensional convection-diffusion problem
In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator...
Optimal control of combined therapy in a single strain HIV-1 model.
Optimal Lyapunov inequalities and applications to nonlinear problems
Optimality and existence for Lipschitz equations.
Optimization of the principal eigenvalue of the one-dimensional Schrödinger operator.