Search Results - "Řehák, Pavel"

Half-linear differential equations: Regular variation, principal solutions, and asymptotic classes by Řehák, Pavel

“…We are interested in the structure of the solution space of second-order half-linear differential equations taking into account various classifications…”
Get full text

Kummer test and regular variation by Řehák, Pavel

“…We establish relations among the Kummer test, certain generalization of discrete regular variation, and regular variation on time scales. More precisely, we…”
Get full text

De Haan type increasing solutions of half-linear differential equations by Řehák, Pavel

“…We study asymptotic behavior of eventually positive increasing solutions to the half-linear equation (r(t)|y′|α−1sgny′)′=p(t)|y|α−1sgny, where r,p are positive…”
Get full text

Decaying positive global solutions of second order difference equations with mean curvature operator by Dosla, Zuzana, Matucci, Serena, Řehák, Pavel

“…A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of…”
Get full text

On decaying and asymptotically constant solutions of nonlinear equations with the Weyl fractional derivative of an order in (1,2) by Řehák, Pavel

“…We consider a sublinear fractional differential equation of an order in the interval (1,2) where the fractional derivative is of the Weyl type. Existence and…”
Get full text

PECULIARITIES IN POWER TYPE COMPARISON RESULTS FOR HALF-LINEAR DYNAMIC EQUATIONS by ŘEHÁK, PAVEL

“…We look for conditions guaranteeing that oscillatory properties of the half-linear dynamic equation (r(t)|yΔ|p-1sgn yΔ)Δ + c(t)|yσ|p-1sgn yσ = 0, p > 1, are…”
Get full text

Asymptotic behavior of increasing solutions to a system of nonlinear differential equations by Aehak, Pavel

“…We consider the system x i a2 = a i (t) | x i + 1 | alpha i sgn x i + 1 , i = 1 , aBB , n , n aY 2 , where a i , i = 1 , aBB , n , are positive continuous…”
Get full text

A precise asymptotic description of half‐linear differential equations by Řehák, Pavel

“…We study asymptotic behavior of solutions of nonoscillatory second‐order half‐linear differential equations. We give (in some sense optimal) conditions that…”
Get full text

Asymptotics of perturbed discrete Euler equations in the critical case by Řehák, Pavel

“…We consider the difference equation Δ2y(k)+p(k)y(k+1)=0 under the condition limk→∞⁡k2p(k)=1/4; such a setting can cover various perturbations of the critical…”
Get full text

Nonlinear Poincaré–Perron theorem by Řehák, Pavel

“…We establish a nonlinear extension of the Poincaré–Perron theorem for a second order half-linear differential equation. Conditions are established which…”
Get full text

On decreasing solutions of second order nearly linear differential equations by ehak, Pavel

“…We consider the nonlinear equation ( r ( t ) G ( y ′ ) ) ′ = p ( t ) F ( y ) , where r , p are positive continuous functions and F ( | ⋅ | ) , G ( | ⋅ | ) are…”
Get full text

The Karamata integration theorem on time scales and its applications in dynamic and difference equations by Řehák, Pavel

“…We derive a time scale version of the well-known result from the theory of regular variation, namely the Karamata integration theorem. We show an application…”
Get full text

Asymptotic formulae for solutions of half-linear differential equations by Řehák, Pavel

“…We establish asymptotic formulae for regularly varying solutions of the half-linear differential equation(r(t)|y′|α−1sgny′)′=p(t)|y|α−1sgny,where r, p are…”
Get full text

An asymptotic analysis of nonoscillatory solutions of q-difference equations via q-regular variation by Řehák, Pavel

“…We do a thorough asymptotic analysis of nonoscillatory solutions of the q-difference equation Dq(r(t)Dqy(t))+p(t)y(qt)=0 considered on the lattice {qk:k∈N0},…”
Get full text

Refined discrete regular variation and its applications by Řehák, Pavel

“…We introduce a new class of the so‐called regularly varying sequences with respect to τ and state its properties. This class, on one hand, generalizes…”
Get full text

Asymptotics of decreasing solutions of coupled -Laplacian systems in the framework of regular variation by Matucci, Serena, Řehák, Pavel

“…Under the assumption that the coefficients are regularly varying functions, existence and asymptotic form of strongly decreasing solutions are here studied for…”
Get full text

On asymptotic relationships between two higher order dynamic equations on time scales by Řehák, Pavel

“…We consider the nth order dynamic equations xΔn+p1(t)xΔn−1+⋯+pn(t)x=0 and yΔn+p1(t)yΔn−1+⋯+pn(t)y=f(t,y(τ(t))) on a time scale T, where τ is a composition of…”
Get full text

Asymptotic formulae for solutions of linear second-order difference equations by Rehak, Pavel

“…We study asymptotic behaviour of solutions to the (nonoscillatory) linear difference equation , where are positive sequences defined on . We establish…”
Get full text

q-Karamata functions and second order q-difference equations by Rehak, P., Vítovec, J.

“…In this paper we introduce and study $q$-rapidly varying functions on the lattice $q^{N_0}:=\{q^k:k\in N_0\}$, $q>1$, which naturally extend the recently…”
Get full text

Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations by Řehák, Pavel

“…We consider the system xi′=ai(t)|xi+1|αisgnxi+1, i=1,…,n, n≥2, where ai, i=1,…,n, are positive continuous functions on [a,∞), αi∈(0,∞), i=1,…,n, with α1⋯αn<1,…”
Get full text