Geodesic
Existence of positive solutions for a class of semipositone problems with Kirchhoff operator
Giovany M. Figueiredo1 ; Eugenio Massa2 ; Jefferson A. Santos3
1 Universidade de Brasília, Departamento de Matemática
2 Universidade de São Paulo - Campus de São Carlos, Departamento de Matemática
3 Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 655-666.

Voir la notice de l'article provenant de 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

Giovany M. Figueiredo 1 ; Eugenio Massa 2 ; Jefferson A. Santos 3

1 Universidade de Brasília, Departamento de Matemática
2 Universidade de São Paulo - Campus de São Carlos, Departamento de Matemática
3 Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática 
@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},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2021},
     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
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a4/
LA  - en
ID  - AFM_2021_46_2_a4
ER  - 
%0 Journal Article
%A Giovany M. Figueiredo
%A Eugenio Massa
%A Jefferson A. Santos
%T Existence of positive solutions for a class of semipositone problems with Kirchhoff operator
%J Annales Fennici Mathematici
%D 2021
%P 655-666
%V 46
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a4/
%G en
%F AFM_2021_46_2_a4
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/