Existence of positive solutions for nonlinear systems

This paper deals with the existence of positive solutions for the nonlinear system q(t)\phi(p(t)u’{i}(t)))‘+f^{i}(t,$\mathbf{\text{u}}$)=0,\quad 0<t<1,\quad i=1,2,…,n. This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here $\mathbf{\text{u}}=(u_1,\mathrm{.}\mathrm{.}\mathrm{.},u_n)$ and $f^{i}, i=1,2,…,n$arecontinuousandnonnegativefunctions,$p(t), q(t)\hbox{\rm :} [0,1]\to (0,\oo)$ are continuous functions. Moreover, we characterize the eigenvalue intervals for (q(t)\phi(p(t)u’{i}(t)))'+\lambda h_{i}(t)g^{i} ($\mathbf{\text{u}}$)=0, \quad 0<t<1,\quad i=1,2,…,n. The proof is based on a well-known fixed point theorem in cones.