Eigenvalues of Fourth-Order Boundary Value Problems with Self-Adjoint Canonical Boundary Conditions
Fourth-order boundary value problems with general real self-adjoint boundary conditions are investigated. It is obtained that the eigenvalues of the problem depend not only continuously on all parameters of the problem but also smoothly on the boundary conditions. Furthermore, the derivatives of the eigenvalues with respect to boundary conditions are given in the sense of the fundamental canonical forms of fourth-order self-adjoint boundary conditions including each type of separated, mixed and coupled cases.
KeywordsFourth-order boundary value problems Eigenvalues Differential expression Self-adjoint canonical boundary conditions
Mathematics Subject ClassificationPrimary 34B05 34B09 Secondary 65L10 65L15
We thank the referees for their careful reading of the manuscript and for making a number of suggestions which have improved the presentation of this paper. This work was supported by National Natural Science Foundation of China (Grant Nos. 11661059, 11301259), Natural Science Foundation of Inner Mongolia (Grant No. 2017JQ07).
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