An Application of a Nonlinear Krein-Rutman Theorem to a Semi-linear Elliptic System

作者：Qi, Zexin^*

来源：Results in Mathematics, 2016, 70(1-2): 127-135.

DOI：10.1007/s00025-015-0466-y

• Semi-linear elliptic system
• Krein-Rutman theorem

This paper is focused on the use of a nonlinear Krein-Rutman theorem to the semi-linear elliptic system
{-Delta u = lambda u(alpha)-v(gamma), x is an element of Omega,
-Delta v = lambda u(delta)v beta, x is an element of Omega,
u(x) = 0, v(x) > 0, x is an element of Omega,
u(x) = v(x) = 0, x is an element of partial derivative Omega} where Omega is a bounded smooth domain in R-N. The parameters are assumed nonnegative and satisfy 0 <= alpha < 1, 0 <= beta< 1 with gamma(delta) = ( 1 - alpha)( 1 - beta). Under these assumptions we show there exists lambda(star) > 0, such that the above system has a classical solution if and only if lambda = lambda(star).

• 出版日期2016-9
• 单位河南师范大学