MULTIPLICITY OF POSITIVE SOLUTIONS FOR A GRADIENT SYSTEM WITH AN EXPONENTIAL NONLINEARITY

作者：Megrez Nasreddine^*; Sreenadh K; Khaldi Brahim

来源：Electronic Journal of Differential Equations, 2012, 236.

• Gradient system
• exponential nonlinearity
• multiplicity

In this article, we consider the problem %26lt;br%26gt;-Delta u = lambda u(q) + f(1)(u, v) in Omega %26lt;br%26gt;-Delta v = lambda v(q) + f(2)(u, v) in Omega %26lt;br%26gt;u, v %26gt; 0 in Omega u = v = 0 on partial derivative Omega, %26lt;br%26gt;where Omega is a bounded domain in R-2, 0 %26lt; q %26lt; 1, and lambda %26gt; 0. We show that there exists a real number Lambda such that the above problem admits at least two solutions for lambda is an element of (0, Lambda), and no solution for lambda %26gt; Lambda.

• 出版日期2012-12-26