Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/1904.03520 |
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Sommario:
- We consider the following quasilinear Schrödinger equations of the form \begin{equation*} \triangle u-\varepsilon V(x)u+u\triangle u^2+u^{p}=0,\ u>0\ \mbox{in}\ \mathbb{R}^N\ \mbox{and}\ \underset{|x|\rightarrow \infty}{\lim} u(x)=0, \end{equation*} where $N\geq 3,$ $p>\frac{N+2}{N-2},$ $\varepsilon>0$ and $V(x)$ is a positive function. By imposing appropriate conditions on $V(x),$ we prove that, for $\varepsilon=1,$ the existence of infinity many positive solutions with slow decaying $O(|x|^{-\frac{2}{p-1}})$ at infinity if $p>\frac{N+2}{N-2}$ and, for $\varepsilon$ sufficiently small, a positive solution with fast decaying $O(|x|^{2-N})$ if $\frac{N+2}{N-2}<p<\frac{3N+2}{N-2}.$ The proofs are based on perturbative approach. To this aim, we also analyze the structure of positive solutions for the zero mass problem.