A non-local semilinear eigenvalue problem
Tóm tắt
We prove that positive solutions of the fractional Lane–Emden equation with homogeneous Dirichlet boundary conditions satisfy pointwise estimates in terms of the best constant in Poincaré’s inequality on all open sets, and are isolated in
$$L^1$$
on smooth bounded ones, whence we deduce the isolation of the first non-local semilinear eigenvalue.
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