某四阶微分算子的一个正则性定理
A Regularity Theorem for a Certain Fourth-order Differential Operator
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摘要: 本文给出了某带参数λ的四阶微分算子Bλ的一个正则性定理,由此我们分别获得了关于该算子在“非线性情形”的二个同胚类及在“线性情形”的三个线性同构类。这对描述某飞行器在其运行过程中某些类双向稳定性质是有用与方便的。Abstract: This paper provides a regularity theorem for certain fourth-order differential operator Bλ with λ. from which we have obtained two homoeomorphism classes in "nonlinear case" or three linear isomorphism classes in "linear case" about this operator respectively It is useful and convenient to explain certain types of stability properties in both directions of some flying vehiele in its moving process.
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Key words:
- homeomorphism /
- linear isomorphism /
- interpolating inequality
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[1] A. L. Greensite, Analysis and Design of Space Vehicle Flight, Control System, Spartan, New York(1970). [2] W. T. Raid, A comparison theorem for selfadjoint differential equations of second order, Ann. Math. 65(1957), 197-202. [3] T. Kusano and B. Singh, Positive solution of functional differential equations with singular nonlinear terms, Nonlinear Analysis, 8(1984), 1081-1090. [4] F. C. Titcltmarch. Eigenfunction Eapensions Associated with Second-Order Differential Equations, Oxford Universtity Press, London(1955). [5] R. A. Admas, Sobolev Space, Springer-Verlag, New York(1975). [6] J. Wloka, Patial Differential Equations, Cambridge University Press, London(1987). [7] V. Barbu, Nonlinear Semigroups and Differential Equatons in Banach Space, Noordhoff, Leyden(1976). -
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