On the Uniqueness of Sign Changing Bound State Solutions of a Semilinear Equation - Yarur-Said, C (Elsevier Masson SAS, 2011)
We establish the uniqueness of the higher radial bound state solutions of?u+f(u)=0,x?Rn. We assume that the nonlinearity f?C(-?,?) 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,?). © 2011 Elsevier Masson SAS.