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I am quite used to "counting"/computing finite dimensions. For example, one would expect a hypersurface in $\mathbb{C}^3$ to have dimension $3 - 1 = 2$. But it is often the case that the ...

Is there any result on the existence of solutions of differential equations of the form $$ D_\alpha\Phi([u])=U_\alpha([u])\Phi([u]), $$ where $[u]$ is an element of an infinite dimensional bundle $J^\...