We prove the existence of standing waves to the following family of nonlinear Sch\"odinger equations: $${\bf i}\hbar \partial_t \psi= - \hbar^2 \Delta \psi + V(x) \psi - \psi|\psi|^{p-2}, \hbox{ } (t, x)\in {\mathbf R} \times {\mathbf R}^n$$ provided that $\hbar>0$ is small, $2<p<\frac{2n}{n-2}$ when $n\geq 3$, $2<p<\infty$ when $n=1,2$ and $V(x)\in L^\infty({\mathbf R}^n)$ is assumed to have a sublevel with positive and finite measure.
Standing waves for a class of nonlinear Schr"odinger equations with potentials in $L^infty$.
PRINARI, Francesca Agnese;
2008
Abstract
We prove the existence of standing waves to the following family of nonlinear Sch\"odinger equations: $${\bf i}\hbar \partial_t \psi= - \hbar^2 \Delta \psi + V(x) \psi - \psi|\psi|^{p-2}, \hbox{ } (t, x)\in {\mathbf R} \times {\mathbf R}^n$$ provided that $\hbar>0$ is small, $2File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
