An expansion result for a Sturm-Liouville eigenvalue problem with impulse
Şerife Faydaoğlu, Gusein Sh. Guseinov · TURKISH JOURNAL OF MATHEMATICS · 2010
The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.