On the uniqueness of sign changing bound state solutions of a semilinear equation

Details On the uniqueness of sign changing bound state solutions of a semilinear equation On the uniqueness of sign changing bound state solutions of a semilinear equation

2010-01-26

arxiv.org/abs/1001.4729v1

Mathematics

Analysis of PDEs

Scientific paper

We establish the uniqueness of the higher radial bound state solutions of $$ \Delta u +f(u)=0,\quad x\in \RR^n. \leqno(P) $$ We assume that the nonlinearity $f\in C(-\infty,\infty)$ is an odd function satisfying some convexity and growth conditions, and either has one zero at $b>0$, is non positive and not identically 0 in $(0,b)$, and is differentiable and positive $[b,\infty)$, or is positive and differentiable in $[0,\infty)$.

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