Electron. J. Differential Equations, Vol. 2017 (2017), No. 146, pp. 1-95.

Characterization of constant sign Green's function for a two-point boundary-value problem by means of spectral theory

Alberto Cabada, Lorena Saavedra

Abstract:
This article is devoted to the study of the parameter's set where the Green's function related to a general linear nth-order operator, depending on a real parameter, T_n[M], coupled with many different two point boundary value conditions, is of constant sign. This constant sign is equivalent to the strongly inverse positive (negative) character of the related operator on suitable spaces related to the boundary conditions.

Submitted January 19, 2017. Published June 22, 2017.
Math Subject Classifications: 34B05, 34B08, 34B27, 34L05, 34B15, 34B18, 47A05.
Key Words: Green's functions; spectral theory; boundary value problems

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Alberto Cabada
Instituto de Matemáticas
Facultade de Matemáticas
Universidade de Santiago de Compostela
Santiago de Compostela, Galicia Spain
email: alberto.cabada@usc.es
Lorena Saavedra
Instituto de Matemáticas
Facultade de Matemáticas
Universidade de Santiago de Compostela
Santiago de Compostela, Galicia Spain
email: lorena.saavedra@usc.es

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