| Abstract: |
| This talk deals with existence and multiplicity results of positive solutions for the quasilinear Schr\odinger equation
\begin{align*}
\left\{\begin{array}{c}
\displaystyle-\Delta u-\lambda m(x) u\Delta(u^2)=f(\mu,x,u)\text{ in }\Omega, \
u=0\text{ on }\partial\Omega.
\end{array}\right.
\end{align*}
where $\Omega$ is a bounded open domain in $\mathbb{R}^N$ with smooth boundary and $m$ is bounded positive continuous function. Under suitable assumptions on $f$ and asymptotically linear behaviour, we can use bifurcation theory in order to give an analysis on the set of positive solutions. |
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