Such a value is called an eigenvalue and the corresponding nontrivial solutions y are called eigenfunctions. Problem 5 isnt, although some authors use a definition of sturmliouville problem that does include it. Pdf the solutions of sturmliouville boundaryvalue problem for. We were able to find the eigenvalues of problems 14 explicitly because in each problem the coefficients in the boundary conditions satisfy \\alpha\beta0\ and \\rho\delta. We would like to generalize some of those techniques in order to solve other boundary. In sturmliouville theory, we say that the multiplicity of an eigenvalue of a sturmliouville problem l. Variational techniques for sturmliouville eigenvalue problems. In this section we will introduce the sturmliouville eigen value problem as a general class of boundary value problems containing the legendre and bessel equations and supplying the theory needed to solve a variety of problems. In this chapter we study sturmliouville boundary value problems and fourier series. It is shown see for example 45 that the eigenvalues of certain leftdefinite.
Some new results concerning general weighted regular sturm. We formulate a selfadjoint qdifference operator in a. Sturmliouville theory american mathematical society. A nonzero function y that solves the sturmliouville problem pxy.
When we solve partial differential equations with boundary conditions by. The next example begins with a scalar problem, problem b, with a general, coupled. Most of our proofs are adapted from 1 and are given using variational methods. Eigenvalue problems, sturmliouville boundary value problems. The boundaryvalue problem only allows nontrivial solu. The text is the same but the format has been modified to fit. Pdf this paper is devoted to studying a qanalogue of sturmliouville eigenvalue problems. The eigenvalues of a sturmliouville problem are all. Computing eigenvalues of regular sturmliouville problems emis. Sturmliouville twopoint boundary value problems 3 we bring 28.
Such functions can be used to represent functions in fourier series expansions. This kind of problem also occurs in many other applications. Numerical computation of sturmliouville problem with. It is also possible to show that the eigenfunctions of the boundary value problem 1, 2 are real.
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