Existence of positive solutions for a class of semipositone problems with Kirchhoff operator - Figueiredo, Giovany M.; Massa, Eugenio; Santos, Jefferson A. (Annales Fennici Mathematici, 2021)
In this work we show a result of existence of positive solution for the following nonlocal problem of Kirchhoff type \(-M(_Ω | abla u|^2 dx)Δ u= f(u)-a\) in \(Ω\), \(u=0\) on \(Ω,\) where \(Ω R^N\) 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.