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Given $k\in\mathbb N$, we define a class of continuous piecewise functions$f$ having abrupt but controlled magnitude changes so that the problem $$\Deltau +f(u)=0,\quad x\in \mathbb R^N, N> 2, $$ has at least $k$ radially symmetricground state solutions.

Multiplicity results for ground state solutions of a semilinear equation via abrupt changes in magnitude of the nonlinearity