Abstract
We present sufficient conditions for the invertibility of a second-order differential operator with variable coefficients in the space Lp.
References
Yu. L. Daletskii and M. G. Krein,Stability of Solutions of Differential Equations in Banach Spaces [in Russian], Nauka, Moscow (1970).
J. B. Massera and J. J. Schäffer,Linear Differential Equations and Function Spaces, Academic Press, New York (1966).
B. M. Levitan and V. V. Zhikov,Almost Periodic Functions and Differential Equations [in Russian], Moskow University, Moscow (1978).
B. F. Bylov, R. É. Vinograd, D. M. Grobman, and V. V. Nemytskii,Theory of Lyapunov Indices and Its Applications to Problems of Stability [in Russian], Nauka, Moscow (1966).
V. I. Rozhkov, “Almost periodic solutions of linear systems with a small parameter multiplying the derivative,”Differents. Uravn.,22, No. 10, 1829–1833 (1986).
A. G. Baskakov and V. V. Yurgelas, “Indefinite dissipativity and invertibility of linear differential operators,”Ukr. Mat. Zh.,41, No. 12, 1613–1618 (1989).
S. L. Édel'shtein, “Operator analogs of WKB-type estimates and solvability of boundary-value problems,”Mat. Zametki,51, No. 4, 124–131 (1992).
A. G. Baskakov, Reducibility of linear differential operators with unbounded operator coefficients,”Ukr. Mat. Zh.,45, No. 5, 587–595 (1993).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 411–413, March, 1995.
This paper was partially supported by the International Science Foundation, Grant No. ZA000.
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Baskakov, A.G., Chernyshov, M.K. On the invertibility of differential operators of the second order. Ukr Math J 47, 477–480 (1995). https://doi.org/10.1007/BF01056311
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DOI: https://doi.org/10.1007/BF01056311