On quasilinear elliptic equations in ℝN

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.

Keywords

• Quasilinear elliptic equation
• p-Laplacian
• variational method.