On the stability of the Ritz procedure for nonlinear two-point boundary value problems
On the step-type contrast structure of a second-order semilinear differential equation with integral boundary conditions.
On the structure of the set of solutions of a functional equation with applications to boundary value problems
On the structure of the set of solutions of nonlinear boundary value problems for ODEs on unbounded intervals
On the symmetric solutions to a class of nonlinear PDEs
On the three-point boundary-value problem for a non-linear third order ordinary differential equation
On the transformation theory of ordinary second-order linear symmetric differential expressions
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-point boundary value problems for two-dimensional differential systems with singularities.
On two-points boundary value problems for ordinary nonlinear differential equations of the fourth order in the Colombeau algebra
On unbounded solutions for differential equations with mean curvature operator
We present necessary and sufficient conditions for the existence of unbounded increasing solutions to ordinary differential equations with mean curvature operator. The results illustrate the asymptotic proximity of such solutions with those of an auxiliary linear equation on the threshold of oscillation. A new oscillation criterion for equations with mean curvature operator, extending Leighton criterion for linear Sturm-Liouville equation, is also derived.
On uniqueness conditions for decreasing solutions of semilinear elliptic equations.
On Urabe's application of Newton's method to nonlinear boundary value problems
On vanishing at infinity of solutions of ordinary differential equations