On radial solutions for singular combined superlinear elliptic systems on annular domains (Q321774)

The authors consider the ODE system NEWLINE\[NEWLINE\begin{aligned} - (r^{N-1} \phi_1(u')'=\lambda r^{N-1} f_1(v), \quad a<r<b,\\ - (r^{N-1} \phi_2(v')'=\lambda r^{N-1} f_2(u), \quad a<r<b \end{aligned}NEWLINE\]NEWLINE and look for sufficient conditions to guarantee the existence of large positive solutions satisfying the boundary conditions NEWLINE\[NEWLINEu(a)=u(b)=v(a)=v(b)=0NEWLINE\]NEWLINE when the parameter \(\lambda\) is small enough. The main tool that they use is a fixed point theorem in cones.