Sentence examples for varying endpoints from inspiring English sources

It is a generalization of [[1], Theorems 3.2 and 3.3] to jointly varying endpoints.

The next result is a generalization of [[1], Corollary 3.12] to jointly varying endpoints.

It generalizes [[1], Theorem 2.8] to jointly varying endpoints, compare also with [[25], Theorem 2.2].

The following statement generalizes [[1], Lemma 2.10] to jointly varying endpoints.

In this paper we develop the spectral theory for discrete symplectic systems with general jointly varying endpoints.

The new transformation of jointly varying endpoints into separated endpoints will also find applications in the continuous time problems or time scales problems (see, e.g., [15]).

Remark 4.10 The augmentation of system ( S λ ) into double dimension is a known technique for studying the problems with jointly varying endpoints; see, e.g., [10 15].

The results of this paper (see Theorem 2.3) also imply the existence of multiple eigenvalues for scalar symplectic eigenvalue problems with jointly varying endpoints.