Existence of positive solutions for a class of semipositone problems with Kirchhoff operator
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 655-666
Cet article a éte moissonné depuis la source Journal.fi
In this work we show a result of existence of positive solution for the following nonlocal problem of Kirchhoff type
$-M\biggl(\int_{\Omega} |\nabla u|^{2} dx\biggl)\Delta u= f(u)-a$ in $\Omega$, $u=0$ on $\partial\Omega,$
where $\Omega \subset\mathbf{R}^{N}$ is a smooth bounded domain, $M,f$ are continuous nonnegative functions and $a>0$. By using mainly variational methods, we prove the existence of a solution for $a$ small enough, under two different sets of hypotheses, which generalize the classical superlinear and sublinear problems.
Keywords:
Nonlocal elliptic problems, degenerate problems, variational methods, positive solutions
Affiliations des auteurs :
Giovany M. Figueiredo 1 ; Eugenio Massa 2 ; Jefferson A. Santos 3
@article{AFM_2021_46_2_a4,
author = {Giovany M. Figueiredo and Eugenio Massa and Jefferson A. Santos},
title = {Existence of positive solutions for a class of semipositone problems with {Kirchhoff} operator},
journal = {Annales Fennici Mathematici},
pages = {655--666},
year = {2021},
volume = {46},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a4/}
}
TY - JOUR AU - Giovany M. Figueiredo AU - Eugenio Massa AU - Jefferson A. Santos TI - Existence of positive solutions for a class of semipositone problems with Kirchhoff operator JO - Annales Fennici Mathematici PY - 2021 SP - 655 EP - 666 VL - 46 IS - 2 UR - http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a4/ LA - en ID - AFM_2021_46_2_a4 ER -
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Giovany M. Figueiredo; Eugenio Massa; Jefferson A. Santos. Existence of positive solutions for a class of semipositone problems with Kirchhoff operator. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 655-666. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a4/