Variational formulation of a damped Dirichlet impulsive problem

被引：83
|
作者：
Nieto, Juan J. [1 ]
机构：
[1] Univ Santiago de Compostela, Fac Matemat, Dept Anal Matemat, E-15782 Santiago, Spain
来源：
APPLIED MATHEMATICS LETTERS | 2010年 / 23卷 / 08期
关键词：
Lax-Milgram theorem; Variational formulation; Critical point; Dirichlet boundary condition; Impulsive differential equation;
D O I：
10.1016/j.aml.2010.04.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this letter we introduce the concept of a weak solution for a damped linear equation with Dirichlet boundary conditions and impulses. We use the classical Lax-Milgram Theorem to reveal the variational structure of the problem and get the existence and uniqueness of weak solutions as critical points. This will allow us in the future to deal with the corresponding nonlinear problems and look for solutions as critical points of weakly lower semicontinuous functionals. (c) 2010 Elsevier Ltd. All rights reserved.
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页码：940 / 942
页数：3
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