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Upper and lower solutions satisfying the inverse inequality

100%

Rachůnková I.

Annales Polonici Mathematici

1996-1997

tom 65

nr 3

235-244

We consider multipoint and two-point BVPs for second order ordinary differential equations with a Carathéodory right hand side. We prove the existence of solutions provided there exist upper and lower solutions of the BVP and the upper solution is less than the lower one.

Minimal κ-connected Graphs with Small Number of Vertices of Degree κ

75%

Karpov D. V.

Fundamenta Informaticae

2016

tom Vol. 145, nr 3

279--312

Nirenberg-type problems in Banach lattices

63%

Duma A. , Duma I.

Journal of Applied Analysis

2010

tom Vol. 16, nr 2

189-197

A slightly modified version of the celebrated Nirenberg problem concerning expanding maps is considered. A positive answer is given for a type of lattice-expansive operators in discrete Hilbert lattices. Our approach is motivated by the study of the infinite systems of nonlinear equations.

The connectivity and compactness of solution set of an integral equation and weak solution set of an initial-boundary value problem

63%

Hoa L. , Ngoc L.

Demonstratio Mathematica

2006

tom Vol. 39, nr 2

357-376

In this paper we show that the set of solutions to the following integral equation.

On the topological dimension of the solutions sets for some classes of operator and differential inclusions

63%

Bader R. , Gel'man B. , Kamenskii M. , Obukhovskii V.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2002

tom 22

nr 1

17-32

In the present paper, we give the lower estimation for the topological dimension of the fixed points set of a condensing continuous multimap in a Banach space. The abstract result is applied to the fixed point set of the multioperator of the form $𝓕 = S 𝓟_F$ where $𝓟_F$ is the superposition multioperator generated by the Carathéodory type multifunction F and S is the shift of a linear injective operator. We present sufficient conditions under which this set has the infinite topological dimension. In the last section of the paper, we consider the applications of the solutions sets for Cauchy and periodic problems for semilinear differential inclusions in a Banach space.

On some topological methods in theory of neutral type operator differential inclusions with applications to control systems

63%

Kamenskii M. , Obukhovskii V. , Yao J.-C.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2013

tom 33

nr 2

193-204

We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.