Abstract
A system of ordinary differential equations of mixed order on an interval (0, r(0)) is considered, where some coefficients are singular at 0. Special cases have been dealt with by KAKO, where the essential spectrum of an operator associated with a linearized MHD model was calculated, and more recently by HARDT, MENNICKEN and NABOKO. In both papers this operator is a selfadjoint extension of an ...
Abstract
A system of ordinary differential equations of mixed order on an interval (0, r(0)) is considered, where some coefficients are singular at 0. Special cases have been dealt with by KAKO, where the essential spectrum of an operator associated with a linearized MHD model was calculated, and more recently by HARDT, MENNICKEN and NABOKO. In both papers this operator is a selfadjoint extension of an operator on sufficiently smooth functions. The approach in the present paper is different in that a suitable operator associated with the given system of ordinary differential equations is explicitly defined as the closure of an operator defined on sufficiently smooth functions. This closed operator can be written as a sum of a selfadjoint operator and a bounded operator. It is shown that its essential spectrum is a nonempty compact subset of C, and formulas for the calculation of the essential spectrum in terms of the coefficients are given.
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