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The applications of Saddle point theorem to Dirichlet boundary value problem of differential system
Author(s) -
Ge Weigao,
Tian Yu
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2997
Subject(s) - mathematics , saddle point , boundary value problem , saddle , dirichlet problem , mathematical analysis , dirichlet boundary condition , dirichlet distribution , order (exchange) , picard–lindelöf theorem , fixed point theorem , matrix (chemical analysis) , pure mathematics , comparison theorem , geometry , mathematical optimization , materials science , finance , economics , composite material
We study in this paper the Dirichlet boundary value problem of second‐order differential system in the formu ′ ′ + Mu + ∇ F ( t , u ) = 0 ,u ( 0 ) = A , u ( 1 ) = B ,where u ∈ R n , A , B ∈ R n , M ∈ R n × n is a symmetric matrix, F : [0,1] × R n → R n such a system comes from a model describing the vibration of a multi‐storey building. By using the saddle point theorem, we prove an existence theorem for the solutions to the given system. Copyright © 2014 John Wiley & Sons, Ltd.
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