Displaying similar documents to “Asymptotic behavior of solutions to half-linear q -difference equations.”

Second order linear q -difference equations: nonoscillation and asymptotics

Pavel Řehák (2011)

Czechoslovak Mathematical Journal

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The paper can be understood as a completion of the q -Karamata theory along with a related discussion on the asymptotic behavior of solutions to the linear q -difference equations. The q -Karamata theory was recently introduced as the theory of regularly varying like functions on the lattice q ℕ 0 : = { q k : k ∈ ℕ 0 } with q > 1 . In addition to recalling the existing concepts of q -regular variation and q -rapid variation we introduce q -regularly bounded functions and prove many related properties. The q -Karamata theory...

Decaying Regularly Varying Solutions of Third-order Differential Equations with a Singular Nonlinearity

Ivana Kučerová (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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This paper is concerned with asymptotic analysis of strongly decaying solutions of the third-order singular differential equation x ' ' ' + q ( t ) x - γ = 0 , by means of regularly varying functions, where γ is a positive constant and q is a positive continuous function on [ a , ∞ ) . It is shown that if q is a regularly varying function, then it is possible to establish necessary and sufficient conditions for the existence of slowly varying solutions and regularly varying solutions of (A) which decrease to 0 as t → ∞ and...