| Abstract: |
| We will study the radially symmetric solutions to the problem
$$ \Delta u+f(u)=0,\quad x\in \mathcal{R}^N, N> 2, \lim_{|x|\to \infty} u(x)=0. $$
We will see that we can generate new solutions to this problem by introducing abrupt magnitude changes in the function $f$.
Using this idea, we can construct functions $f$, defined by parts, such that the problem has any given number of solutions. |
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