Radialization and Fake Distances

The proof of some of our main results, for instance the (CSP), relies on the construction of a suitable radial solution of (P≥) or (P≤) to be compared with a given one. For convenience, hereafter we extend φ to an odd function on all of \(\mathbb R\) by setting $$\displaystyle \varphi (s) = - \varphi (-s) \qquad \text{for each } \, s<0. $$

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