On quasilinear elliptic equations in $\mathbb{R}^N$

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 $-\Delta u=h\left(x\right)u^q$ in ${ℝ}^N$, where , 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.