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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 instability of nonlinear differential equations.

Avis, Rafael, Naulin, Raúl (1997)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Asymptotic integration of a nonhomogeneous differential equation with integrable coefficients

Thomas G. Hallam (1971)

Czechoslovak Mathematical Journal

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 $t \to \infty$ .

Asymptotic invariant sets of autonomous differential equations

Bihari, I. (1979)

Equadiff IV

Asymptotic methods for singularly perturbed linear differential equations in Banach spaces

Mika, Janusz (1979)

Equadiff IV

Asymptotic nature of solutions of the equation $\dot{z} = f (t, z)$ with a complex valued function $f$

Josef Kalas (1984)

Archivum Mathematicum

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.