MULTIPLE SOLUTIONS FOR CRITICAL ELLIPTIC SYSTEMS VIA PENALIZATION METHOD

作者：Alves Claudianor O^*; Figueiredo Giovany M; Furtado Marcelo F

来源：Differential and Integral Equations, 2010, 23(7-8): 703-723.

We consider the system
{-epsilon(2) Delta u + W(x)u = Q(u)(u,v) + 1/2* Ku(u,v) in R(N),
-epsilon(2) Delta v + W(x)v = Q(v)(u,v) + 1/2* Ku(u,v) in R(N),
u,v is an element of H(1) (R(N)), u(x), v(x) > 0 for each x is an element of R(N),
where 2* = 2N/(N - 2), N >= 3, epsilon > 0 is a parameter, W and V are positive potentials, and Q and K are homogeneous function with K having critical growth. We relate the number of solutions to the topology of the set where W and V attain their minimum values. In the proof, we apply Ljusternik-Schnirelmann theory.

• 出版日期2010-8