International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 364085, 25 pages
doi:10.1155/2008/364085

On the Existence of Solutions of a Nonlocal Elliptic Equation with a p-Kirchhoff-Type Term

Francisco Julio S.A. Corrêa1 and Rúbia G. Nascimento2

1Unidade Acadêmica de Matemática e Estatística, Centro de Ciências Tecnologia, Universidade Federal de Campina Grande, 58.109-970, Campina Grande, PB, Brazil
 2Campus do Baixo Tocantins, Universidade Federal do Pará, 68.440-000 Abaetetuba, PA, Brazil

Abstract

Questions on the existence of positive solutions for the following class of elliptic problems are studied: −[M(‖u‖1,pp)]1,pΔpu=f(x,u), in Ω, u=0, on ∂Ω, where Ω⊂ℝN is a bounded smooth domain, f:Ω¯×ℝ+→ℝ and M:ℝ+→ℝ,  ℝ+=[0,∞) are given functions.