On the stability of radial solutions of semilinear elliptic equations in all of R n

@inproceedings{Cabr2008OnTS,
  title={On the stability of radial solutions of semilinear elliptic equations in all of R n},
  author={Xavier Cabr{\'e} and Antonio Capella},
  year={2008}
}
We establish that every nonconstant bounded radial solution u of −∆u = f(u) in all of R is unstable if n ≤ 10. The result applies to every C nonlinearity f satisfying a generic nondegeneracy condition. In particular, it applies to every analytic and every power-like nonlinearity. We also give an example of a nonconstant bounded radial solution u which is stable for every n ≥ 11, and where f is a polynomial. Sur la stabilité des solutions radiales des équations elliptiques semilinéaires dans… CONTINUE READING
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