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On the finiteness of the Morse Index for Schrödinger operators
the Morse Index Schrö dinger operators
2010/11/19
Let H=$\Delta +V$ be a Schr\"odinger on a complete non-compact manifold. It is known since the work of Fischer-Colbrie and Schoen that the finiteness of the negative spectrum of $H$ implies the exist...
Multiple Solutions and Its Morse Index for One-Dimensional Nonlinear Problem
Nonlinear problem multiple solutions series expression Morse index
2007/12/11
The multiple solutions for one-dimensional cubicnonlinear problem $u''+u^3=0,u(0)=u(\pi)=0$ are computed, on thebasis of the eigenpairs of $-\phi''_k=\lambda_k \phi_k, \ k=1,2,3\cdots$. There exist t...