Existence of solutions for a class of damped vibration problems on time scales
type: Item
instance of: scholarly article
title: Existence of solutions for a class of damped vibration problems on time scales
zbMATH Open document ID: 1216.34102
DOI: 10.1155/2010/727486
author: Jianwen Zhou
author: Yongkun Li
published in: Advances in Difference Equations
publication date: 2011-02-08T00:00:00Z
full work available at URL: https://eudml.org/doc/229163
review text: The authors present in detail the concepts on time scales which are available in the standard book written by Martin Bohner and A. C. Peterson. The time scale is an interesting area of current research as it unifies both continuous and discrete concepts. The authors consider a class of damped vibration problem on time scales with periodic boundary conditions. The authors use recent methods of variational methods and critical point theory for establishing the existence of solution to the above two point boundary value problem. By taking a variational structure of the problem, the authors reduce the problem of finding solutions to the two point boundary value problem to the one of a corresponding functional. The results of the paper are illustrated with some suitable examples. These results are extension of their previous paper published in [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No.~5, 1375--1388 (2010; Zbl 1201.46035)].
reviewed by: K. Rajendra Prasad
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 5847742
zbMATH Keywords: damped vibration problem
zbMATH Keywords: time scale
zbMATH Keywords: variational method
zbMATH Keywords: critical point theory
Wikidata QID: Q59253431
MaRDI profile type: Publication
OpenAlex ID: W2002667813
cites work: Q5751214
cites work: Q4716262
cites work: Q2723195
cites work: Infinite interval problems for differential, difference and integral equations
cites work: Q4797834
cites work: Q4466556
cites work: Q4829684
cites work: Basic calculus on time scales and some of its applications
cites work: Integration on time scales.
cites work: Q4462026
cites work: Periodic solutions for a neutral nonlinear dynamical equation on a time scale
cites work: Basic properties of Sobolev's spaces on time scales
cites work: Existence of positive periodic solutions for functional differential equations with impulse effects on time scales
cites work: Existence and approximation of extremal solutions to first-order infinite systems of functional dynamic equations
cites work: Multiple positive solutions of singular Dirichlet problems on time scales via variational methods
cites work: Existence theory for positive solutions to one-dimensional \(p\)-Laplacian boundary value problems on time scales
cites work: Existence of positive solutions for singular boundary value problem on time scales
cites work: Existence of weak solutions of two-point boundary value problems for second-order dynamic equations on time scales
cites work: Sturm-Liouville eigenvalue problems on time scales
cites work: \(L^{2}\) spaces and boundary value problems on time-scales
cites work: Eigenfunction expansions in \(L^{2}\) spaces for boundary value problems on time-scales
cites work: Sobolev's spaces on time scales and its applications to a class of second order Hamiltonian systems on time scales
cites work: Critical point theory and Hamiltonian systems
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description: scientific article; zbMATH DE number 5847742