Spektrum of special Laplace type operator - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T06:55:04Z http://mathoverflow.net/feeds/question/75752 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75752/spektrum-of-special-laplace-type-operator Spektrum of special Laplace type operator Kofi 2011-09-18T14:39:37Z 2011-09-18T14:39:37Z <p>How can I find Eigenvalues of the differential operator $-\frac{d^2}{dt^2} + \mathrm{sin} =\Delta + \mathrm{sin}$, defined on $M=S^1$, the 1-Sphere?</p> <p>It seems that the underlying ODE is pretty much unsolvable explicitly, but after all I am only interested in the Eigenvalues, not the Eigenfunctions itself, so there might be some other way?</p> <p>I am also interested in functions $v \in C^\infty(S^1)$ such that the EV of $\Delta + v$ can be computed easily, but I was not able to find any nonconstant ones yet.</p>