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Asymptotic estimates of solutions and their derivatives for n-th order nonhomogeneous ordinary differential equations with constant coefficients

Jan Andres, Tomá Turský (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Asymptotic estimates of solutions and their derivatives for n-th order nonhomogeneous ODEs with constant coefficients are obtained, provided the associated characteristic polynomial is (asymptotically) stable. Assuming, additionally, the stability of the so called "shifted polynomials" (see below) to the characteristic one, the estimates can be still improved.

Asymptotic forms of solutions of perturbed half-linear ordinary differential equations

Sokea Luey, Hiroyuki Usami (2021)

Archivum Mathematicum

Asymptotic forms of solutions of half-linear ordinary differential equation ( | u ' | α - 1 u ' ) ' = α ( 1 + b ( t ) ) | u | α - 1 u are investigated under a smallness condition and some signum conditions on b ( t ) . When α = 1 , our results reduce to well-known ones for linear ordinary differential equations.

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 .

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