MULTIPLICITY OF SOLUTIONS FOR BIHARMONIC ELLIPTIC SYSTEMS INVOLVING CRITICAL NONLINEARITY

作者：Lu Dengfeng^*; Xiao Jianhai

来源：Bulletin of the Korean Mathematical Society, 2013, 50(5): 1693-1710.

DOI：10.4134/BKMS.2013.50.5.1693

• biharmonic elliptic system
• critical Sobolev exponent
• variational method
• multiple solutions

In this paper, we consider the biharmonic elliptic systems of the form
{Delta(2)u = Fu(u,v) + lambda vertical bar u vertical bar(q-2)u, x is an element of Omega, Delta(2)v = Fv (u, v) + delta vertical bar v vertical bar(q-2)v, x is an element of Omega, u = partial derivative u/partial derivative n = 0, v = partial derivative v/partial derivative n = 0, x is an element of partial derivative Omega,
where Omega subset of R-N is a bounded domain with smooth boundary partial derivative Omega, Delta(2) is the biharmonic operator, N >= 5,2 <= q < 2*, 2* = 2N/N-4 denotes the critical Sobolev exponent, F is an element of C-1 (R-2, R+) is homogeneous function of degree 2*. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on lambda and delta.

• 出版日期2013-9
• 单位湖北工程学院