Existence of entire radial large solutions for a class of Monge–Ampère type equations and systems

Abstract

This paper is mainly concerned with existence of entire positive radial large solutions for a class of Monge–Ampère type equations: det D 2 u ( x ) − α Δ u = a ( | x | ) f ( u ) , x ∈ ℝ N , and systems: det D 2 u ( x ) − α Δ u = a ( | x | ) f ( v ) , x ∈ ℝ N , det D 2 v ( x ) − β Δ v = b ( | x | ) g ( u ) , x ∈ ℝ N , where detD2u is the so-called Monge–Ampère operator, Δ is the classical Laplace operator, N≥2, α,β are positive constants, f,g:[0,∞)→[0,∞) are continuous and nondecreasing, and a,b:ℝN→[0,∞) are continuous.