Levine, Howard A. Some uniqueness and growth theorems in the Cauchy problem for \(Pu_{tt}+Mu_t+Nu=0\) in Hilbert space. (English) Zbl 0238.35016 Math. Z. 126, 345-360 (1972). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 8 Documents MSC: 35G10 Initial value problems for linear higher-order PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35B45 A priori estimates in context of PDEs 47F05 General theory of partial differential operators PDFBibTeX XMLCite \textit{H. A. Levine}, Math. Z. 126, 345--360 (1972; Zbl 0238.35016) Full Text: DOI EuDML References: [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). · Zbl 0097.08101 · doi:10.1002/cpa.3160130402 [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). · Zbl 0226.34056 [5] Murray, A.C.: Asymptotic behavior of solutions of hyperbolic inequalities. Trans. Amer. Math. Soc.157, 279-296 (1971). · Zbl 0214.10403 · doi:10.1090/S0002-9947-1971-0274922-5 [6] Ogawa, H.: Lower bounds for solutions of hyperbolic inequalities. Proc. Amer. Math. Soc.16, 853-857 (1965). · Zbl 0138.34804 · doi:10.1090/S0002-9939-1965-0193376-3 [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). · Zbl 0218.34059 [9] Love, A.E.H.: A freatise on the mathematical theory of Elasticity. Dover, 1944. · Zbl 0063.03651 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.