On the uniqueness of sign changing bound state solutions of a semilinear equation
Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 4, p. 599-621
We establish the uniqueness of the higher radial bound state solutions of Δu+f(u)=0,x n .(P) We assume that the nonlinearity fC(-,) is an odd function satisfying some convexity and growth conditions, and has one zero at b>0, is nonpositive and not-identically 0 in (0,b), positive in [b,), and is differentiable in (0,).
@article{AIHPC_2011__28_4_599_0,
     author = {Cort\'azar, Carmen and Garc\'\i a-Huidobro, Marta and Yarur, Cecilia S.},
     title = {On the uniqueness of sign changing bound state solutions of a semilinear equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {28},
     number = {4},
     year = {2011},
     pages = {599-621},
     doi = {10.1016/j.anihpc.2011.04.002},
     zbl = {1236.35056},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2011__28_4_599_0}
}
Cortázar, Carmen; García-Huidobro, Marta; Yarur, Cecilia S. On the uniqueness of sign changing bound state solutions of a semilinear equation. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 4, pp. 599-621. doi : 10.1016/j.anihpc.2011.04.002. http://www.numdam.org/item/AIHPC_2011__28_4_599_0/

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