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On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints

Adel Mahmoud Gomaa (2012)

Czechoslovak Mathematical Journal

We deal with the problems of four boundary points conditions for both differential inclusions and differential equations with and without moving constraints. Using a very recent result we prove existence of generalized solutions for some differential inclusions and some differential equations with moving constraints. The results obtained improve the recent results obtained by Papageorgiou and Ibrahim-Gomaa. Also by means of a rather different approach based on an existence theorem due to O. N. Ricceri...

On noncompact perturbation of nonconvex sweeping process

Myelkebir Aitalioubrahim (2012)

Commentationes Mathematicae Universitatis Carolinae

We prove a theorem on the existence of solutions of a first order functional differential inclusion governed by a class of nonconvex sweeping process with a noncompact perturbation.

On positive solutions for a nonlinear boundary value problem with impulse

Huseyin Bereketoglu, Aydin Huseynov (2006)

Czechoslovak Mathematical Journal

In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.

On solvability of nonlinear boundary value problems for the equation ( x ' + g ( t , x , x ' ) ) ' = f ( t , x , x ' ) with one-sided growth restrictions on f

Staněk, Svatoslav (2002)

Archivum Mathematicum

We consider boundary value problems for second order differential equations of the form ( x ' + g ( t , x , x ' ) ) ' = f ( t , x , x ' ) with the boundary conditions r ( x ( 0 ) , x ' ( 0 ) , x ( T ) ) + ϕ ( x ) = 0 , w ( x ( 0 ) , x ( T ) , x ' ( T ) ) + ψ ( x ) = 0 , where g , r , w are continuous functions, f satisfies the local Carathéodory conditions and ϕ , ψ are continuous and nondecreasing functionals. Existence results are proved by the method of lower and upper functions and applying the degree theory for α -condensing operators.

On some alternative forms equivalent to Kruskal's condition for OLSE to be BLUE.

Gabriela Beganu (2007)

RACSAM

The necessary and sufficient condition for the ordinary least squares estimators (OLSE) to be the best linear unbiased estimators (BLUE) of the expected mean in the general univariate linear regression model was given by Kruskal (1968) using a coordinate-free approach. The purpose of this article is to present in the same manner some alternative forms of this condition and to prove two of the Haberman’s equivalent conditions in a different and simpler way. The results obtained in the general univariate...

On some nonlinear alternatives of Leray-Schauder type and functional integral equations

Bapurao Chandra Dhage (2006)

Archivum Mathematicum

In this paper, some new fixed point theorems concerning the nonlinear alternative of Leray-Schauder type are proved in a Banach algebra. Applications are given to nonlinear functional integral equations in Banach algebras for proving the existence results. Our results of this paper complement the results that appear in Granas et. al. (Granas, A., Guenther, R. B. and Lee, J. W., Some existence principles in the Caratherodony theory of nonlinear differential system, J. Math. Pures Appl. 70 (1991),...

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