Open AccessThe unbounded solution of a periodic mixed Sturm–Liouville problem in an infinite strip for the Laplacian
Author(s) -
M. G. El-Sheikh,
V. Gavdzinski,
Tarek Emam
Publication year - 2013
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.04.006
Subject(s) - mathematics , algebraic number , dirichlet distribution , semi infinite , sturm–liouville theory , truncation (statistics) , mathematical analysis , neumann boundary condition , algebraic equation , type (biology) , boundary value problem , pure mathematics , nonlinear system , ecology , statistics , physics , quantum mechanics , biology
The unbounded solution, at the points where the boundary conditions change, for a mixed Sturm–Liouville problem of the Dirichlet–Neumann type can be obtained using the method of the integral equation formulation. Since this formulation is usually reduced to an infinite algebraic system in which the unknowns are the Fourier coefficients of the unknown unbounded entity, a study of ℓp-solutions imposes itself concerning the influence of the truncation on such systems. This study is achieved and the well-known theorem on the ℓ2-solutions of the infinite algebraic systems is generalized