The Sturm-Liouville operator on the space of functions with discontinuity conditions

The Sturm-Liouville differential operators defined on the space of discontinuous functions, where the moments of discontinuity of the functions are interior points of the interval and the discontinuity conditions are linear have been studied. Auxiliary results concerning the Green's formula, boundary value, and eigenvalue problems for impulsive differential equations are emphasized.


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A Rayleigh–Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schrödinger equation -y″(x)+v(x)y(x)=λy(x),x∈(-∞,∞) has been converted into an integral equation. For a regular problem, the unbounded interval is truncated to x∈ [ - ℓ, ℓ] , where ℓ is regarded as a boundary parameter. Then, the resulting integral equation has been solved and the results are co...
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Citation Formats
Ö. Uğur, “The Sturm-Liouville operator on the space of functions with discontinuity conditions,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 889–896, 2006, Accessed: 00, 2020. [Online]. Available: