| Abstract: |
| We present a novel approach to study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schr\odinger equation of the form
\begin{equation*}
-\Delta u+\lambda u=g(u), \quad u \in H^1(\RN), \, N \geq 1.
\end{equation*}
This approach permits to handle in a unified way nonlinearities $g(s)$ which are either mass subcritical, mass critical or mass supercritical. Among its main ingredients is the study of the asymptotic behaviors of the positive solutions as $\lambda\rightarrow 0^+$ or $\lambda\rightarrow +\infty$ and the existence of an unbounded continuum of solutions in $(0, + \infty) \times H^1(\RN)$. This talk is based on joint work with Prof. Louis Jeanjean and Prof. Xuexiu Zhong. |
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