An expansion result for a Sturm-Liouville eigenvalue problem with impulse

Authors: ŞERİFE FAYDAOĞLU, GUSEIN SH. GUSEINOV

Abstract: 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.

Keywords: Green's function; Completely continuous operator; Impulse conditions; Eigenvalue; Eigenvector.

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