• Positive Solutions and Eigenvalue Intervals for Nonlinear Systems

• # Fulltext

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

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

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.

• # Author Affiliations

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

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019