Discontinuous Sturm-Liouville operator~ with boundary condition depending on the spectral parameter and indefinite weight function is studied. Firstly, a Krein space and a new operator~ related to the boundary-value problem are constructed to make the eigenvalues of the operators~ and~ same. It is proved that the operator~ is self-adjoint in the space ~. Then, by studying the spectral distribution of the operator~, it is shown
that all the eignvalues of the boundary value problem are real, there exist countably infinitely many positive and negative eigenvalues, and they are unbounded from below and from above, have no finite cluster point, and can be written as Finally, a specific example is given to get the eigenvalues distribution.
ZHAO Yingchun, SUN Jiong. , {{custom_author.name_en}}.
DISCONTINUOUS STURM-LIOUVILLE OPERATOR WITH BOUNDARY CONDITION CONTAINING THE SPECTRAL PARAMETER AND INDEFINITE WEIGHT FUNCTION. Journal of Systems Science and Mathematical Sciences, 2011, 31(5): 597-613 https://doi.org/10.12341/jssms11613