A few remarks on Poincaré-Perron solutions and regularly varying solutions
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Pavel Řehák
Abstract
We establish conditions guaranteeing the existence of (generalized) regularly varying solutions to nth order linear differential and q-difference equations. The proofs are based mainly on classical Poincaré’s and Perron’s theorems and certain transformations. In some special cases, our results reduce to the existing ones, thus actually we offer an alternative approach to some parts of the asymptotic theory of differential equations made in the framework of regular variation. For higher order cases, our statements are essentially new. Another important feature of this paper is that it reveals connections among various results and somehow revises some of them.
This work was supported by the grant 201/10/1032 of the Czech Science Foundation and by RVO 67985840
Acknowledgements
The author thanks the both referees for their careful reading of the manuscript and helpful comments.
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© 2016 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
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- A few remarks on Poincaré-Perron solutions and regularly varying solutions
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- On the internal approach to differential equations 3. Infinitesimal symmetries
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- Wick differential and Poisson equations associated to the 𝚀𝚆𝙽-Euler operator acting on generalized operators
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- On codes over 𝓡k, m and constructions for new binary self-dual codes
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Artikel in diesem Heft
- A triple representation of lattice effect algebras
- Periods of morgan-voyce sequences and elliptic curves
- Multiplicative generalized derivations on ideals in semiprime rings
- A few remarks on Poincaré-Perron solutions and regularly varying solutions
- Applications of extremal theorem and radius equation for a class of analytic functions
- On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions
- New criteria for global exponential stability of linear time-varying volterra difference equations
- On approximation of functions by some hump matrix means of Fourier series
- Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras
- Poisson kernels on semi-direct products of abelian groups
- Locally convex projective limit cones
- On the properties (wL) and (wV)
- On the existence of solutions for quadratic integral equations in Orlicz spaces
- Existence and uniqueness of best proximity points under rational contractivity conditions
- Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds
- On the internal approach to differential equations 3. Infinitesimal symmetries
- A Characterization of the discontinuity point set of strongly separately continuous functions on products
- Wick differential and Poisson equations associated to the 𝚀𝚆𝙽-Euler operator acting on generalized operators
- Multivariate EIV models
- On codes over 𝓡k, m and constructions for new binary self-dual codes
- Domination number of total graphs
