A variational approach for standing waves of FitzHugh-Nagumo type systems

作者：Chen Chao Nien; Tanaka Kazunaga^*

来源：Journal of Differential Equations, 2014, 257(1): 109-144.

DOI：10.1016/j.jde.2014.03.013

We study the existence of radially symmetric solutions of FitzHugh-Nagumo type elliptic systems in R-N (N >= 2):
-Delta u=g(u)-v in R-N, -d Delta v+gamma v = u in R-N, (*) (u(x),v(x))-> (0,0) as vertical bar x vertical bar -> infinity.
We utilize a truncation technique and apply minimax arguments to the corresponding strongly indefinite functional
I-gamma (u,v) = 1/2 integral(RN) vertical bar del u vertical bar(2) - d vertical bar del v vertical bar(2) dx - integral(RN)G(u) + gamma/2 v(2) -uv dx,
defined on H-r(1)(R-N) x H-r(1)(R-N), to find positive and possibly sign-changing solutions of (*). In particular, we overcome difficulty related to Palais Smale condition via our new scaling argument. When g(xi) = xi(1-xi)(xi-alpha), alpha is an element of (0, 1/2), we improve the existence result of Reinecke Sweers [23].

• 出版日期2014-7-1