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    • 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

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