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The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem

Mieczysław Cichoń, Ireneusz Kubiaczyk, Sikorska-Nowak, Aneta Sikorska-Nowak, Aneta (2004)

Czechoslovak Mathematical Journal

In this paper we prove an existence theorem for the Cauchy problem x ' ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x 0 , t I α = [ 0 , α ] using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of measures of weak noncompactness.

The impact of unbounded swings of the forcing term on the asymptotic behavior of functional equations

Bhagat Singh (2000)

Czechoslovak Mathematical Journal

Necessary and sufficient conditions have been found to force all solutions of the equation ( r ( t ) y ' ( t ) ) ( n - 1 ) + a ( t ) h ( y ( g ( t ) ) ) = f ( t ) , to behave in peculiar ways. These results are then extended to the elliptic equation | x | p - 1 Δ y ( | x | ) + a ( | x | ) h ( y ( g ( | x | ) ) ) = f ( | x | ) where Δ is the Laplace operator and p 3 is an integer.

The inverse carrier problem

Grant B. Gustafson, Miroslav Laitoch (2002)

Czechoslovak Mathematical Journal

The problem was motivated by Borůvka’s definitions of the carrier and the associated carrier. The inverse carrier problem is precisely defined and partially solved. Examples are given.

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