On the existence of nonnegative radial solutions for elliptic systems (Q2735427)

The authors consider the nonlinear elliptic system \(\Delta u+p(r) f(u)=0\), \(0<A<r<B\), with one of the following sets of boundary conditions NEWLINE\[NEWLINEu=0\text{ on }r=A\text{ and }r=B;NEWLINE\]NEWLINE NEWLINE\[NEWLINEu=0\text{ on }r=A,\text{ and }{\partial u\over\partial r}=0\text{ on }r=B;NEWLINE\]NEWLINE NEWLINE\[NEWLINE{\partial u\over\partial r}=0\text{ on }r=A,\text{ and }u=0\text{ on }r=B,NEWLINE\]NEWLINE with \(r=\sqrt{x^2_1+ x^2_{2}+ \cdots+ x^2_n}\), \(p(r)f(u)= (p_1(r)f_1(u), \dots,p_m (r)f_m(u))\), \(m\geq 1\). They show the existence of nonnegative radial solutions when \(f\) is either superlinear or sublinear. The proofs are based on Krasnoselskii's fixed-point theorem. Their results extend the main results by the reviewer [J. Math. Anal. Appl. 201, No. 2, 375-386 (1996; Zbl 0859.35040)].