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1. Asymptotic properties for half-linear difference equations

Creator:
Cecchi, Mariella, Došlá, Zuzana, Marini, Mauro, and Vrkoč, Ivo
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
half-linear second order difference equation, nonoscillatory solutions, Riccati difference equation, and summation inequalities
Language:
English
Description:
Asymptotic properties of the half-linear difference equation (∗) ∆(an|∆xn| α sgn ∆xn) = bn|xn+1| α sgn xn+1 are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to (∗) are considered too. Our approach is based on a classification of solutions of (∗) and on some summation inequalities for double series, which can be used also in other different contexts.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

8. Resonance and multiplicity in periodic boundary value problems with singularity

Creator:
Rachůnková, Irena, Tvrdý, Milan, and Vrkoč, Ivo
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
second order nonlinear ordinary differential equation, periodic problem, and lower and upper functions
Language:
English
Description:
The paper deals with the boundary value problem u '' + k u = g(u) + e(t), u(0) = u(2π), u ' (0) = u ' (2π), where k ∈ R, g : (0, ∞) → R is continuous, e ∈ L[0, 2π] and lim x→0+ ∫1 x g(s) ds = ∞. In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public