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.
FAYDAOĞLU, ŞERİFE and GUSEINOV, GUSEIN SH.
"An expansion result for a Sturm-Liouville eigenvalue problem with impulse,"
Turkish Journal of Mathematics: Vol. 34:
3, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol34/iss3/6