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Search Results: 1 - 10 of 913 matches for " Irena Rach nková "
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Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential Equation
Irena Rach nková,Luká Rach nek
Abstract and Applied Analysis , 2011, DOI: 10.1155/2011/981401
Abstract: Singular differential equation (())=()() is investigated. Here is Lipschitz continuous on ℝ and has at least two zeros 0 and >0 . The function is continuous on [0,∞) and has a positive continuous derivative on (0,∞) and (0)=0. An asymptotic formula for oscillatory solutions is derived.
Strictly Increasing Solutions of Nonautonomous Difference Equations Arising in Hydrodynamics
Rach?nek Luká?,Rachnková Irena
Advances in Difference Equations , 2010,
Abstract: The paper provides conditions sufficient for the existence of strictly increasing solutions of the second-order nonautonomous difference equation , , where is a parameter and is Lipschitz continuous and has three real zeros . In particular we prove that for each sufficiently small there exists a solution such that is increasing, and . The problem is motivated by some models arising in hydrodynamics.
Nonmonotone impulse effects in second-order periodic boundary value problems
Irena Rach nková,Milan Tvrdy
Abstract and Applied Analysis , 2004, DOI: 10.1155/s1085337504306299
Abstract: We deal with the nonlinear impulsive periodic boundary valueproblem u″=f(t,u,u′), u(ti
Nonlinear systems of differential inequalities and solvability of certain boundary value problems
Rachnková Irena,Tvrdy Milan
Journal of Inequalities and Applications , 2001,
Abstract: In the paper we present some new existence results for nonlinear second order generalized periodic boundary value problems of the form These results are based on the method of lower and upper functions defined as solutions of the system of differential inequalities associated with the problem and their relation to the Leray–Schauder topological degree of the corresponding operator. Our main goal consists in a fairly general definition of these functions as couples from . Some conditions ensuring their existence are indicated, as well.
A new approach to BVPs with state-dependent impulses
Irena Rach nková and Jan Tome ek
Boundary Value Problems , 2013, DOI: 10.1186/1687-2770-2013-22
Abstract: MSC: 34B37, 34B15.
Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations
Rachnková Irena,Tome?ek Jan
Boundary Value Problems , 2009,
Abstract: This paper investigates the singular differential equation , having a singularity at . The existence of a strictly increasing solution (a homoclinic solution) satisfying , is proved provided that has two zeros and a linear behaviour near .
Superlinear Singular Problems on the Half Line
Rachnková Irena,Tome?ek Jan
Boundary Value Problems , 2010,
Abstract: The paper studies the singular differential equation , which has a singularity at . Here the existence of strictly increasing solutions satisfying is proved under the assumption that has two zeros 0 and and a superlinear behaviour near . The problem generalizes some models arising in hydrodynamics or in the nonlinear field theory.
Existence of Oscillatory Solutions of Singular Nonlinear Differential Equations
Irena Rach nková,Luká Rach nek,Jan Tome ek
Abstract and Applied Analysis , 2011, DOI: 10.1155/2011/408525
Abstract: Asymptotic properties of solutions of the singular differential equation (()())=()(()) are described. Here, f is Lipschitz continuous on ℝ and has at least two zeros 0 and >0. The function p is continuous on [0, ∞) and has a positive continuous derivative on (0, ∞) and (0)=0. Further conditions for f and p under which the equation has oscillatory solutions converging to 0 are given.
Oscillatory Solutions of Singular Equations Arising in Hydrodynamics
Rachnková Irena,Tome?ek Jan,Stryja Jakub
Advances in Difference Equations , 2010,
Abstract: We investigate the singular differential equation on the half-line [), where satisfies the local Lipschitz condition on and has at least two simple zeros. The function is continuous on [) and has a positive continuous derivative on () and . We bring additional conditions for and under which the equation has oscillatory solutions with decreasing amplitudes.
Superlinear Singular Problems on the Half Line
Irena Rachůnková,Jan Tomeček
Boundary Value Problems , 2010, DOI: 10.1155/2010/429813
Abstract:
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