Roland Lemmert

Gewöhnliche Differentialgleichungen mit quasimonoton wachsenden rechten Seiten in geordneten Banachräumen

In General Inequalities 5, Ray Redheffer and two authors of the present paper have given an existence theorem for ordinary differential equations, where the right hand side is assumed to be monotone increasing. The main objective here is to prove the same result with monotonicity replaced by quasimonotonicity. Moreover, we consider variable order cones.

Ein Existenzsatz für Gewöhnliche Differentialgleichungen in Geordneten Banachräumen

An existence theorem for ordinary differential equations in Banach spaces will be given, where the right hand side is monotone increasing with respect to a cone.

Bifurcation of periodic solution in a three-unit neural network with delay

A system of three-unit networks with no self-connection is investigated, the general formula for bifurcation direction of Hopf bifurcation is calculated, and the estimation formula of the period for periodic solution is given.

One-sided estimates for quasimonotone increasing functions

Let E be a Banach space ordered by a solid and normal cone K , and normed by the Minkowski functional of an order interval [– p , p ], p ∈ K ∘ . We derive global one-sided estimates for quasimonotone increasing functions f : [0, T ) × E → E with respect to the norm, and the distance to the line generated by p , under conditions of f ; in direction p .

Singular nonlinear boundary value problems

We study nonlinear singular Sturm-Liouville bondary value prob lems associated with the operator , special cases of which come up in connection with the radial Laplace operator, and prove existence and uniqueness theorems under asymptotic non- resonance conditions on the slope of the nonlinear term with respect to the dependent variable. For the underlying linear problems is allowed; nevertheless they have a pure point spectrum as in the classical case. In our treatment the Prufer transformation plays an essential role. Our results apply in the case where Dirchlets problem with radial data is considered in a ball, whereas this problem on an annulus leads to regular Sturm-Liouville problems.

The shooting method for some nonlinear Sturm-Liouville boundary value problems

AbstractThe shooting method is used to prove existence and uniqueness of the solution for a semilinear Sturm-Liouville boundary value problem (N).

An existence theorem for systems of boundary value problems

\frac{\partial }{{\partial u}}f(x,u)

A ONE-SIDED VERSION OF A THEOREM OF KANTOROVICH

“lies between two consecutive eigenvalues” of the related linear problem, the shooting function turns out to be strongly monotone.