Skip to main content
SpringerLink
Log in

Some uniqueness and growth theorems in the Cauchy problem forPu tt +Mu t +Nu=0 in Hilbert space

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliography

  1. Agmon, S.: Unicité et convexité dans les problèmes différentiels. Sem. Math. Sup. (1965), Univ. of Montreal Press (1966).

  2. John, F.: Continuous dependence on data for solutions of partial differential equations with a prescribed bound. Commun. Pure Appl. Math.13, 551–585 (1960).

    Google Scholar 

  3. Levine, H.A.: Logarithmic convexity and the Cauchy problem forP(t)u tt +M(t)u t +N(t)u=0 in Hilbert space. Battelle (Geneva) Adv. Studies Centre, Report 49, Sept. 1971.

  4. Levine, H.A.: On the uniqueness of bounded solutions tou′(t)=A(t)u(t) andu″(t)=A(t)u(t) in Hilbert space. SIAM J. on Analysis (In Print).

  5. Murray, A.C.: Asymptotic behavior of solutions of hyperbolic inequalities. Trans. Amer. Math. Soc.157, 279–296 (1971).

    Google Scholar 

  6. Ogawa, H.: Lower bounds for solutions of hyperbolic inequalities. Proc. Amer. Math. Soc.16, 853–857 (1965).

    Google Scholar 

  7. Protter, M.H.: Asymptotic behavior and uniqueness theorem for hyperbolic equations and inequalities. Proc. of U.S.-U.S.S.R., Symposium on partial differential equations Novosibirsk (1963), 348–353.

  8. Zaidman, S.: Uniqueness of bounded solutions for some abstract differential equations. Ann. Univ. Ferrara, Sez. VII (N. S.)14, 101–104 (1969).

    Google Scholar 

  9. Love, A.E.H.: A freatise on the mathematical theory of Elasticity. Dover, 1944.

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 55455, Minneapolis, Minnesota, USA

    Howard A. Levine

Authors
  1. Howard A. Levine
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The support of this research by the Battelle Advanced Studies Center of Geneva, Switzerland, is gratefully acknowledged.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Levine, H.A. Some uniqueness and growth theorems in the Cauchy problem forPu tt +Mu t +Nu=0 in Hilbert space. Math Z 126, 345–360 (1972). https://doi.org/10.1007/BF01110339

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01110339

Keywords

Search

Navigation