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.


An eigenfunction expansion for the Schrodinger equation with arbitrary non-central potentials
Taşeli, Hasan; Uğur, Ömür (2002-11-01)
An eigenfunction expansion for the Schrodinger equation for a particle moving in an arbitrary non-central potential in the cylindrical polar coordinates is introduced, which reduces the partial differential equation to a system of coupled differential equations in the radial variable r. It is proved that such an orthogonal expansion of the wavefunction into the complete set of Chebyshev polynomials is uniformly convergent on any domain of (r, theta). As a benchmark application, the bound states calculations...
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An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations
Cengizci, Süleyman (Hindawi Limited, 2017)
In thiswork, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, ...
Boundary value problems for higher order linear impulsive differential equations
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Variational iteration method for Sturm-Liouville differential equations
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In this article, He's variational iteration method is applied to linear Sturm-Liouville eigenvalue and boundary value problems, including the harmonic oscillator. In this method, solutions of the problems are approximated by a set of functions that may include possible constants to be determined from the boundary conditions. By computing variations, the Lagrange multipliers are derived and the generalised expressions of variational iterations are constructed. Numerical results show that the method is simple...
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: