Abstract
The continuous dependence of solutions of positive definite, self-adjoint partial differential equations on the domain was investigated by Babugka [I], [2]. In a recent paper, [3], Babugka and Vjibornjr also studied the continuous dependence of the eigenvalues of strongly-elliptic, self-adjoint partial differential operators on the domain. It is the aim of this paper to study formalisms in abstract Hilbert space by means of which results on various types of continuous dependences can be obtained. In the case of the positive definite operator it is found that the condition of self-adjointness can be dropped. The properties of operators of this type are studied in part II. In part III the behavior of the eigenvalues of a selfadjoint elliptic operator under various “small changes” is studied. In part IV some applications to partial differential operators and variational theory are sketched.
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