Abstract
In this article, we consider the second order quasilinear elliptic system of the form piui = Hi(jxj)u i i+1 ; x 2 R N ; i = 1; 2; ; m with nonnegative continuous functions Hi. Sucien t conditions are given to have nonnegative nontrivial radial entire solutions. When Hi; i = 1; 2; ; m, behave like constant multiples of jxj ; 2 R, we can completely characterize the existence property of nonnegative nontrivial radial entire solutions.
Highlights
This paper is concerned with existence and nonexistence of nonnegative radial entire solutions of second order quasilinear elliptic systems of the form
When p = 2, ∆p reduces to the usual Laplacian
As far as the author knows, very little is known about this problem for the system (1.1) except for the case pi = 2, i = 1, 2, · · ·, m
Summary
This paper is concerned with existence and nonexistence of nonnegative radial entire solutions of second order quasilinear elliptic systems of the form (1.1). When f has the form f (|x|, u) = ±H(|x|)uα with α > 0 and positive function H, critical decay rate of H to admit nonnegative radial entire solutions has been characterized. In [12], the author has considered the elliptic system (1.1) with m = 2 and has obtained existence and nonexistence criteria of nonnegative nontrivial radial entire solutions. Theorem 0.1 characterizes the decay rates of H1 and H2 for the system (1.1) to admit nonnegative nontrivial radial entire solutions. Under the assumption (1.2) the system (1.1) has a nonnegative nontrivial radial entire solution if and only if (1.3) holds.
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