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

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.

Anahtar Kelimeler:

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

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

Keywords:

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

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Department of Engineering, Dokuz Eyl¨ul University, Buca, ˙Izmir-TURKEY e-mail: serife.faydaoglu@deu.edu.tr Gusein Sh. GUSEINOV Department of Mathematics, Atilim University, ˙Incek, Ankara-TURKEY e-mail: guseinov@atilim.edu.tr