• Jifeng Chu

Articles written in Proceedings – Mathematical Sciences

• Positive Solutions and Eigenvalue Intervals for Nonlinear Systems

This paper deals with the existence of positive solutions for the nonlinear system

$$(q(t)\phi(p(t){u'}_i(t)))'+f^i(t,u)=0, \quad 0 &lt; t &lt; 1, \quad i=1,2,\ldots,n.$$

This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here $u=(u_1,...,u_n)$ and $f^i,i=1,2,\ldots,n$ are continuous and nonnegative functions, $p(t), q(t):[0, 1]\to(0,\infty)$ are continuous functions. Moreover, we characterize the eigenvalue intervals for

$$(q(t)\phi(p(t){u'}_i(t)))'+\lambda h_i(t)g^i(u)=0,\quad 0 &lt; t &lt; 1, \quad i=1,2,\ldots,n.$$

The proof is based on a well-known fixed point theorem in cones.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019