The Existence and Nonexistence of Entire Positive Radial Solutions of Quasilinear Elliptic Systems with Gradient Term
Hongxia Qin *
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Jiangsu Nanjing 210023, China.
Zuodong Yang
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Jiangsu Nanjing 210023, China.
*Author to whom correspondence should be addressed.
Abstract
We study the existence and nonexistence of entire positive solutions for quasilinear elliptic system
with gradient term
on 
where nonlinearities f and g are positive and continuous, the potentials a and b are continuous, c-positive and satisfy appropriate growth conditions at infinity. We have that entire large positive solutions fail to exist if f and g are sublinear and a and b have fast decay at infinity, while if f and g satisfy some growth conditions at infinity, and a; b are of slow decay or fast decay at infinity, then the system has infinitely many entire solutions, which are large or bounded.
Keywords: Quasilinear elliptic equations, Large solutions, Bounded solution, Entire radial solution