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Sufficient conditions for the existence of a solution to the problem uâ€²â€²(t) = g(t) uÎ¼(t) âˆ’ h(t) uÎ»(t) + f(t) for a. e. t âˆˆ [0, Ï‰], u(0) = u(Ï‰), uâ€²(0) = uâ€²(Ï‰) are established. 2000 Mathematics Subject Classification: 34B18, 34C25

- Robert Hakl
- 2002

Sufficient conditions of the existence and uniqueness of bounded on real axis solutions of systems of linear functional differential equations are established. 1. Formulations of the Main Results Let R be the set of real numbers, Cloc(R, R) be the space of continuous functions u : R â†’ R with the topology of uniform convergence on every compact interval andâ€¦ (More)

1991 Mathematics Subject Classification. 34K10 Key words and phrases. System of linear functional differential equations, linear differential system with deviating arguments, boundary value problem

- Robert Hakl
- 2004

Theorems on the Fredholm alternative and well-posedness of the linear boundary value problem uâ€²(t)= (u)(t) + q(t), h(u)= c, where : C([a,b];R)â†’ L([a,b];R) and h : C([a, b];R)â†’ R are linear bounded operators, q âˆˆ L([a,b];R), and c âˆˆ R, are established even in the case when is not a strongly bounded operator. The question on the dimension of the solutionâ€¦ (More)

- Robert Hakl
- 2005

The following notation is used throughout the paper: N is the set of all natural numbers. R is the set of all real numbers, R+ = [0,+âˆž[,[x]+ = (1/2)(|x|+ x), [x]âˆ’ = (1/2)(|x|âˆ’ x). C([a,b];R) is the Banach space of continuous functions u : [a,b]â†’ R with the norm â€–uâ€–C =max{|u(t)| : t âˆˆ [a,b]}. CÌƒ([a,b];R) is the set of absolutely continuous functions u :â€¦ (More)

Consider the homogeneous equation u â€²(t) = l(u)(t) for a.e. t âˆˆ [a, b] where l : C([a, b];R) â†’ L([a, b];R) is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficientâ€¦ (More)

Nonimprovable sufficient conditions for the solvability and unique solvability of the problem u(t) = F (u)(t) , u(a) âˆ’ Î»u(b) = h(u) are established, where F : C([a, b];R) â†’ L([a, b];R) is a continuous operator satisfying the CarathÃ¨odory conditions, h : C([a, b];R) â†’ R is a continuous functional, and Î» âˆˆ R+.

- Robert Hakl, Pedro J. Torres
- Applied Mathematics and Computation
- 2011

New criteria for the existence of a maximum or antimaximum principle of a general second order operator with periodic conditions, as well as conditions for nonresonance, are provided and compared with the related literature. The purpose of this paper is to study some qualitative properties of the second order linear operator LÂ½p; qÂŠu u 00 Ã¾ pÃ°tÃžu 0 Ã¾ qÃ°tÃžuâ€¦ (More)

- Karel Segeth, Milan TvrdÃ½, +6 authors Pavel DrÃ¡bek
- 2007

Provider's code AV0 IRP identification code Z10190503 Research plan title Research and development of general mathematical knowledge and its application to other branches of science and practice Applicant 2 Name of the department or applicant's principal organisational unit, which will carry out the research according to the proposal, if different from "â€¦ (More)

- Robert Hakl, Manuel Zamora
- 2012

A well-known theorem proved by A. C. Lazer and S. Solimini claims that the singular equation uâ€²â€² + 1 uÎ» = h(t), Î» > 0, has a periodic solution if and only if the mean value of the continuous external force is positive. In this paper, we show that this result cannot be extended to the case when h is an integrable function, unless the additional assumptionsâ€¦ (More)