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Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices

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Showing a solution of elliptic PDe is non-degenerate

Here I explain where the original problem is coming from, since it is quite possible I don't need what I am asking for. I am interested in obtaining positive solutions of the equation $ -\Delta u( …
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Showing a solution of elliptic PDe is non-degenerate

Dear Mathoverflowers: I am interested in radial positive solutions of $-\Delta u(r) = r^\alpha u(r)^p$ in the unit ball in $ R^N$ with $ u=0$ on the boundary. Here $p>1$ and $ \alpha >0$. (There …
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