• Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/117/01/0085-0095

    • Keywords

       

      Nonlinear system; 𝑝-Laplacian; positive solutions; eigenvalue intervals; fixed point theorem in cones.

    • Abstract

       

      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.

    • Author Affiliations

       

      Jifeng Chu1 2 Donal O'Regan3 Meirong Zhang1

      1. Department of Mathematical Sciences, Tsinghua University, Beijing 100 084, China
      2. Department of Applied Mathematics, Hohai University, Nanjing 210 098, China
      3. Department of Mathematics, National University of Ireland, Galway, Ireland
    • Dates

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.