• Meirong Zhang

      Articles written in Proceedings – Mathematical Sciences

    • Positive Solutions and Eigenvalue Intervals for Nonlinear Systems

      Jifeng Chu Donal O'Regan Meirong Zhang

      More Details Abstract Fulltext PDF

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

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

      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

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

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

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