TY - JOUR
AU - Bartsch, Thomas
AU - Wang, Zhi-Qiang
PY - 1999/06/01
Y2 - 2022/01/20
TI - Sign changing solutions of nonlinear SchrÃ¶dinger equations
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 13
IS - 2
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.1999.010
SP - 191 - 198
AB - We are interested in solutions $u\in H^1({\mathbb R}^N)$ of the linear SchrÃ¶dinger equation$-\delta u +b_{\lambda} (x) u =f(x,u)$. The nonlinearity $f$ growssuperlinearly and subcritically as $\vert u\vert \to\infty$.The potential $b_{\lambda}$ is positive, bounded away from $0$, and has a potential well.The parameter $\lambda$ controls the steepness of the well.In an earlier paper we found a positive and a negative solution.In this paper we find third solution. We also prove that this third solutionchanges sign and that it is concentrated in the potential well if $\lambda \to \infty$.No symmetry conditions are assumed.
ER -