Multiple positive solutions for semilinear elliptic systems

作者：Lin Huei li^*

来源：Journal of Mathematical Analysis and Applications, 2012, 391(1): 107-118.

DOI：10.1016/j.jmaa.2012.02.028

• Semilinear elliptic systems
• Critical exponent
• Nehari manifold

This article investigates the effect of the coefficient f (z) of the critical nonlinearity. For sufficiently small lambda, mu %26gt; 0, there are at least k positive solutions of the semilinear elliptic systems %26lt;br%26gt;{-Delta u = lambda g(z)vertical bar u vertical bar(p-2)u + alpha/alpha+beta f(z)vertical bar u vertical bar(alpha-2)u vertical bar v vertical bar(beta) in Omega: %26lt;br%26gt;-Delta v = mu h(z)vertical bar v vertical bar(p-2)v + beta/alpha+beta f(z)vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta-2) in Omega: %26lt;br%26gt;u = v = 0 on partial derivative Omega. %26lt;br%26gt;where 0 epsilon Omega subset of R-N is a bounded domain, alpha %26gt; 1, beta %26gt; 1 and 2 %26lt; p %26lt; alpha + beta = 2* for N %26gt; 4.

• 出版日期2012-7-1
• 单位长春大学