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188宝金博页面版: Existence of semi-nodal solution for a class of FitzHugh–Nagumo type system

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内容提示: Monatsh Math (2016) 181:515–526DOI 10.1007/s00605-016-0925-xExistence of semi-nodal solution for a classof FitzHugh–Nagumo type systemClaudianor O. Alves 1 · Giovany M. Figueiredo 2 ·Al?nnio B. Nobrega 1Received: 11 July 2015 / Accepted: 11 May 2016 / Published online: 23 May 2016? Springer-Verlag Wien 2016Abstract We show the existence of a semi-nodal solution for a FitzHugh–Nagumosystem of the type??u = f (x,u) ? v in ?, ??v = δu ? γv in ?, u = v = 0 on ??,where ? is a bounded domain in R N...

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Monatsh Math (2016) 181:515–526DOI 10.1007/s00605-016-0925-xExistence of semi-nodal solution for a classof FitzHugh–Nagumo type systemClaudianor O. Alves 1 · Giovany M. Figueiredo 2 ·Alânnio B. Nobrega 1Received: 11 July 2015 / Accepted: 11 May 2016 / Published online: 23 May 2016© Springer-Verlag Wien 2016Abstract We show the existence of a semi-nodal solution for a FitzHugh–Nagumosystem of the type−?u = f (x,u) − v in ?, −?v = δu − γv in ?, u = v = 0 on ∂?,where ? is a bounded domain in R N , δ > 0, γ > 2 √ δ and f is a superlinear C 1function with subcritical growth.Keywords Elliptic system · Variational methods · Nodal solutionMathematics Subject Classif i cation 35J91 · 35A15 · 35B991 IntroductionIn this paper, we study the existence of a semi-nodal solution for the followingproblemCommunicated by A. Constantin.C. O. Alves research was partially supported by INCT-MAT, PROCAD and CNPq/Brazil 301807/2013-2,G. M. Figueiredo was partially supported by CNPq/PQ 302933/2014-0 and 200237/2012-8.B Giovany M. Figueiredogiovany@ufpa.br1Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática,Campina Grande, PB CEP: 58429:900, Brazil2Faculdade de Matemática, Universidade Federal do Pará, Bélem, PA CEP: 66075:110, Brazil123

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