Existence of positive solutions for a class of semipositone problems with Kirchhoff operator

Authors

  • Giovany M. Figueiredo Universidade de Brasília, Departamento de Matemática
  • Eugenio Massa Universidade de São Paulo - Campus de São Carlos, Departamento de Matemática
  • Jefferson A. Santos Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática

Keywords:

Nonlocal elliptic problems, degenerate problems, variational methods, positive solutions

Abstract

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.

 

Section
Articles

Published

2021-08-02

How to Cite

Figueiredo, G. M., Massa, E., & Santos, J. A. (2021). Existence of positive solutions for a class of semipositone problems with Kirchhoff operator. Annales Fennici Mathematici, 46(2), 655–666. Retrieved from https://afm.journal.fi/article/view/110567