# Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities

Commentationes Mathematicae Universitatis Carolinae (2013)

- Volume: 54, Issue: 4, page 485-491
- ISSN: 0010-2628

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topAnello, Giovanni, and Rao, Giuseppe. "Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities." Commentationes Mathematicae Universitatis Carolinae 54.4 (2013): 485-491. <http://eudml.org/doc/260586>.

@article{Anello2013,

abstract = {Let $p>1$, $q>p$, $\lambda >0$ and $s\in ]1,p[$. We study, for $s\rightarrow p^-$, the behavior of positive solutions of the problem $-\Delta _p u = \lambda u^\{s-1\}+u^\{q-1\}$ in $\Omega $, $u_\{\mid \partial \Omega \}=0$. In particular, we give a positive answer to an open question formulated in a recent paper of the first author.},

author = {Anello, Giovanni, Rao, Giuseppe},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {elliptic boundary value problems; positive solutions; variational methods; asymptotic behavior; combined nonlinearities; elliptic boundary value problems; positive solutions; variational methods; asymptotic behavior; combined nonlinearities},

language = {eng},

number = {4},

pages = {485-491},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities},

url = {http://eudml.org/doc/260586},

volume = {54},

year = {2013},

}

TY - JOUR

AU - Anello, Giovanni

AU - Rao, Giuseppe

TI - Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2013

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 54

IS - 4

SP - 485

EP - 491

AB - Let $p>1$, $q>p$, $\lambda >0$ and $s\in ]1,p[$. We study, for $s\rightarrow p^-$, the behavior of positive solutions of the problem $-\Delta _p u = \lambda u^{s-1}+u^{q-1}$ in $\Omega $, $u_{\mid \partial \Omega }=0$. In particular, we give a positive answer to an open question formulated in a recent paper of the first author.

LA - eng

KW - elliptic boundary value problems; positive solutions; variational methods; asymptotic behavior; combined nonlinearities; elliptic boundary value problems; positive solutions; variational methods; asymptotic behavior; combined nonlinearities

UR - http://eudml.org/doc/260586

ER -

## References

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- Moser J., 10.1002/cpa.3160130308, Comm. Pure Appl. Math. 13 (1960), 457–478. Zbl0111.09301MR0170091DOI10.1002/cpa.3160130308

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