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The spectra of general differential operators in the direct sum spaces

Sobhy El-sayed Ibrahim (2004)

Czechoslovak Mathematical Journal

In this paper, the general ordinary quasi-differential expression M p of n -th order with complex coefficients and its formal adjoint M p + on any finite number of intervals I p = ( a p , b p ) , p = 1 , ⋯ , N , are considered in the setting of the direct sums of L w p 2 ( a p , b p ) -spaces of functions defined on each of the separate intervals, and a number of results concerning the location of the point spectra and the regularity fields of general differential operators generated by such expressions are obtained. Some of these are extensions or generalizations...

Three methods for the study of semilinear equations at resonance

Bogdan Przeradzki (1993)

Colloquium Mathematicae

Three methods for the study of the solvability of semilinear equations with noninvertible linear parts are compared: the alternative method, the continuation method of Mawhin and a new perturbation method [22]-[27]. Some extension of the last method and applications to differential equations in Banach spaces are presented.

Universality of derivative and antiderivative operators with holomorphic coefficients

María del Carmen Calderón-Moreno (2001)

Annales Polonici Mathematici

We prove some conditions on a sequence of functions and on a complex domain for the existence of universal functions with respect to sequences of certain derivative and antiderivative operators related to them. Conditions for the equicontinuity of those families of operators are also studied. The conditions depend upon the "size" of the domain and functions. Some earlier results about multiplicative complex sequences are extended.

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