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Asymptotic Fourier and Laplace transformations for hyperfunctions

Michael Langenbruch (2011)

Studia Mathematica

We develop an elementary theory of Fourier and Laplace transformations for exponentially decreasing hyperfunctions. Since any hyperfunction can be extended to an exponentially decreasing hyperfunction, this provides simple notions of asymptotic Fourier and Laplace transformations for hyperfunctions, improving the existing models. This is used to prove criteria for the uniqueness and solvability of the abstract Cauchy problem in Fréchet spaces.

Asymptotic integration of differential equations with singular p -Laplacian

Milan Medveď, Eva Pekárková (2016)

Archivum Mathematicum

In this paper we deal with the problem of asymptotic integration of nonlinear differential equations with p - Laplacian, where 1 < p < 2 . We prove sufficient conditions under which all solutions of an equation from this class are converging to a linear function as t → ∞ .

Asymptotic normality of eigenvalues of random ordinary differential operators

Martin Hála (1991)

Applications of Mathematics

Boundary value problems for ordinary differential equations with random coefficients are dealt with. The coefficients are assumed to be Gaussian vectorial stationary processes multiplied by intensity functions and converging to the white noise process. A theorem on the limit distribution of the random eigenvalues is presented together with applications in mechanics and dynamics.

Asymptotic properties of an unstable two-dimensional differential system with delay

Josef Kalas (2006)

Mathematica Bohemica

The asymptotic behaviour of the solutions is studied for a real unstable two-dimensional system x ' ( t ) = 𝖠 ( t ) x ( t ) + 𝖡 ( t ) x ( t - r ) + h ( t , x ( t ) , x ( t - r ) ) , where r > 0 is a constant delay. It is supposed that 𝖠 , 𝖡 and h are matrix functions and a vector function, respectively. Our results complement those of Kalas [Nonlinear Anal. 62(2) (2005), 207–224], where the conditions for the existence of bounded solutions or solutions tending to the origin as t → ∞ are given. The method of investigation is based on the transformation of the real system considered to one...

Asymptotic properties of differential equations with advanced argument

Jan Čermák (2000)

Czechoslovak Mathematical Journal

The paper discusses the asymptotic properties of solutions of the scalar functional differential equation y ' ( x ) = a y ( τ ( x ) ) + b y ( x ) , x ∈ [ x 0 , ∞ ) of the advanced type. We show that, given a specific asymptotic behaviour, there is a (unique) solution y ( x ) which behaves in this way.

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