Positive Solutions and Eigenvalue Intervals for Nonlinear Systems

Proceedings Mathematical Sciences

Meirong Zhang²  Donal O'Regan¹  Jifeng Chu³ 

[1] Department of Applied Mathematics, Hohai University, Nanjing 0 0, China$$;Department of Mathematics, National University of Ireland, Galway, Ireland$$;Department of Mathematical Sciences, Tsinghua University, Beijing 00 0, China$$

关键词: Nonlinear system;    ð?‘?-Laplacian;    positive solutions;    eigenvalue intervals;    fixed point theorem in cones.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

This paper deals with the existence of positive solutions for the nonlinear system$$(q(t)𝜙(p(t){u'}_i(t)))'+f^i(t,u)=0, quad 0 < t < 1, quad i=1,2,ldots,n.$$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, $p(t), q(t):[0, 1]→(0,∞)$ are continuous functions. Moreover, we characterize the eigenvalue intervals for$$(q(t)𝜙(p(t){u'}_i(t)))'+𝜆 h_i(t)g^i(u)=0,quad 0 < t < 1, quad i=1,2,ldots,n.$$The proof is based on a well-known fixed point theorem in cones.

【 授权许可】

Unknown