TY - JOUR
T1 - A variational approach for standing waves of FitzHugh-Nagumo type systems
AU - Chen, Chao Nien
AU - Tanaka, Kazunaga
N1 - Funding Information:
The first author is supported in part by National Science Council, Taiwan ( NSC 102-2115-M-018-002-MY3 ). The second author is supported in part by Grant-in-Aid for Scientific Research (B) (No. 25287025 ) of Japan Society for the Promotion of Science .
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/7/1
Y1 - 2014/7/1
N2 - We study the existence of radially symmetric solutions of FitzHugh-Nagumo type elliptic systems in RN (N≥2): -δu=g(u)-vin RN,-dδv+γv=uin RN,(u(x),v(x))→(0,0)as |x|→∞. We utilize a truncation technique and apply minimax arguments to the corresponding strongly indefinite functionalIγ(u,v)=12RN|∇ ;u|2-d|∇ ;v|2dx-RNG(u)+γ2v2-uvdx, defined on Hr1(RN)×Hr1(RN), 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(ξ)=ξ(1-ξ)(ξ-α), α∈(0,12), we improve the existence result of Reinecke-Sweers [23].
AB - We study the existence of radially symmetric solutions of FitzHugh-Nagumo type elliptic systems in RN (N≥2): -δu=g(u)-vin RN,-dδv+γv=uin RN,(u(x),v(x))→(0,0)as |x|→∞. We utilize a truncation technique and apply minimax arguments to the corresponding strongly indefinite functionalIγ(u,v)=12RN|∇ ;u|2-d|∇ ;v|2dx-RNG(u)+γ2v2-uvdx, defined on Hr1(RN)×Hr1(RN), 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(ξ)=ξ(1-ξ)(ξ-α), α∈(0,12), we improve the existence result of Reinecke-Sweers [23].
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U2 - 10.1016/j.jde.2014.03.013
DO - 10.1016/j.jde.2014.03.013
M3 - Article
AN - SCOPUS:84899630399
VL - 257
SP - 109
EP - 144
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 1
ER -