ISSN:
1420-9039
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
,
Physik
Notizen:
Abstract Dry friction problems lead to discontinuous differential equations, e.g. to $$x'' + xx' + \mu \operatorname{sgn} x' + \beta ^2 x = \varphi (t),$$ where sgn γ=γγ for γ ≠ 0 and sgn (0)=[ − 1. 1]. We study existence of ω-periodic solutions of (1) in case ϕ is ω-periodic. Results forx〉 0 are given in the book “Multivalued Differential Equations” (K. Deimling: De Gruyter 1992). and preliminary ones forx=0 are contained in K. Deimling “Multivalued differential equations and dry friction problems” (Proc. Conf. Differential & Delay Equations. World Sci. Publ. 1992). Based on the latter and considerable additional analysis, we give a complete description of the resonant casex=0.β=1. ϕ(t)=sint. In particular, it turned out that for μ ε (π 4. 1) there is a unique globally asymptotically stable 2π-periodic solutionx gm, which necessarily has deadzones (i.e.xμ (t) ≡c in certain intervals). In addition, the nonresonant case is solved by means of degree theory for multivalued maps, since in this situation a priori bounds can be found easily.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF00942846
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