摘要:

We study weak formulations of diffusion problems with “dynamical” boundary conditions where the “spatial” differential operator is uniformly strongly elliptic. Separation of time and spatial variables lead to non-coercive quadratic forms, and we introduce the notion ofJ-coercivityto handle this type of problem. The direct method of Courant is employed to prove the validity of the eigenfunction expansions The eigenfunction expansions are then used to construct series solutions of the underlying evolution equations.

ISSN:1607-3606    

DOI:10.1080/16073606.1982.9631878

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

In this paper we connect the function-theoretic properties of the matrix Titchmarsh-Weyl M(λ) function with the spectrum of a linear Hamiltonian system. Characterizations are given for the resolvent set, the point spectrum, the continuous spectrum and the point-continuous spectrum. The Hamiltonian system is considered under a limit-point hypothesis. In section 5 we establish invariance of certain parts of the spectrum with respect to boundary conditions.

ISSN:1607-3606    

DOI:10.1080/16073606.1982.9631879

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

A limit-point criterion for symmetric quasi-differential expressions of arbitrary order with matrix-valued coefficients is given. This criterion is also sufficient for real polynomials in such expressions to be in the limit-point case. In the scalar case it includes a number of known results most of which were proved by asymptotic methods.

ISSN:1607-3606    

DOI:10.1080/16073606.1982.9631880

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1982.9631881

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1982.9631877

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor