Abstract and Applied Analysis
Volume 1 (1996), Issue 4, Pages 407-415
doi:10.1155/S108533759600022X

On quasilinear elliptic equations in ℝN

C. O. Alves,1 J. V. Concalves,2 and L. A. Maia2

1Departamento de Matemática, Universidade Federal da Paraiba, Campina Grande-(PB), 58100-240 -, Brazil
2Departamento de Matemática, Universidade de Brasília, Brasilia 70.910-900, DF, Brazil

Received 15 September 1996

Copyright © 1996 C. O. Alves et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −Δu=h(x)uq in ℝN, where 0<q<1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the existence of solutions.