Abstract
The nonlinear operator is considered, in which is an invertible closed linear operator with an everywhere dense domain of definition in a Banach space , is an analytic operator satisfying strong continuity requirements with respect to the action of as well as the conditions and , and is an auxiliary number greater than one. Local and global theorems are obtained on the representation of in the form , where and are analytic operators, and the real and complex powers are defined. The existence of complex powers is used to obtain an expression for in terms of the , where is a functional. It is proved that the results are applicable to nonlinear elliptic differential operators on spaces of periodic functions.Bibliography: 16 titles.
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