Positive solutions of an elliptic equation involving a sign-changing potential and a gradient term

Abstract

The objective of this paper is to investigate the elliptic singular Laplacian equation Δu−|∇u|q+up−u−δ=0 in RN, where N≥1, 1<q<p and δ>2. Our main contributions consist of establishing the existence of an entire strictly positive solution and analyzing certain properties of its asymptotic behavior, particularly when it exhibits monotonicity.