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