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13 Sturm{Liouville problems. Eigenvalues and eigenfunctions

13 Sturm{Liouville problems. Eigenvalues and eigenfunctionsIn the previous lecture I gave four examples of different boundary value problems for a second orderODE that resulted in a countable number of constants (lambdas) and a countable number of corre-sponding solutions, which were used afterwards to build the corresponding Fourier series to representsolutions for PDE. Not surprisingly, these four examples can be generalized in a relatively abstractframework, which I discuss in this lecture. In the literature this framework is calledSturm Liouvilleproblem after two mathematicians who first concentrated on this start with the definition ofSturm liouville differential operatorLon the intervalx [a;b]:Lu:= (p(x)u ) +q(x)u;( )wherep;qare continuous on [a;b] andp(x)>0 for anyx [a;b].}

13 Sturm{Liouville problems. Eigenvalues and eigenfunctions In the previous lecture I gave four examples of different boundary value problems for a second order

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