A Remark on Singular Perturbation Methods via the Lyapunov-Schmidt Reduction | Zendy

Masaharu Taniguchi | Zendy

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A Remark on Singular Perturbation Methods via the Lyapunov-Schmidt Reduction

Author(s) -

Masaharu Taniguchi

Publication year - 1995

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195163593

Subject(s) - mathematics , lyapunov function , bounded function , perturbation (astronomy) , singular perturbation , reduction (mathematics) , reaction–diffusion system , inverse , lyapunov equation , operator (biology) , mathematical analysis , nonlinear system , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene

For some reaction-diffusion equations, Lyapunov-Schmidt reduction was shown to be applicable to construct singularly perturbed equilibrium solutions. For this application, it is indispensable to show that some inverse operator are uniformly bounded. In this paper, we give an elementary proof of this fact. §

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