On Solutions of <inline-formula><graphic file="1029-242X-2002-325650-i1.gif"/></inline-formula>

Abstract

Rotationally symmetric solutions are derived for some nonlinear equations of the form in the title in terms of elementary functions. Under suitable assumptions, the nonexistence of entire solutions is also proved for the inequality in the title as well as some radial upper bounds are obtained. These results are the consequence of an appropriate differential inequality.

Keywords

• Laplace operator
• Rotationally symmetric solutions
• Entire solutions