Variational approach to differential equations with not instantaneous impulses

被引：72

作者：

Bai, Liang ^{[1
]}

Nieto, Juan J. ^{[2
]}

机构：

[1] Taiyuan Univ Technol, Coll Math, Taiyuan 030024, Shanxi, Peoples R China

[2] Univ Santiago de Compostela, Fac Matemat, Dept Anal Matemat Estadist & Optimizac, Santiago De Compostela 15782, Spain

来源：

APPLIED MATHEMATICS LETTERS | 2017年 / 73卷

关键词：

Non-instantaneous impulse; Variational method; Lax-Milgram theorem; Critical point; Impulsive differential equation; EXISTENCE;

D O I：

10.1016/j.aml.2017.02.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we introduce the concept of a weak solution for a linear equation with not instantaneous 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. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：44 / 48

页数：5

共 16 条

[1]

[Anonymous], 1995, World Sci. Ser. Nonlinear Sci., Ser. A., DOI DOI 10.1142/2892

[2]

[Anonymous], 2014, Nonauton. Dyn. Syst.

[3]

CHIPOT M, 2000, BIRK ADV TEXT, pR7

[4] Existence of solutions for a second-order differential equation with non-instantaneous impulses and delay [J].

Colao, Vittorio ;

Muglia, Luigi ;

Xu, Hong-Kun .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2016, 195 (03) :697-716

[5] The Existence and Multiplicity of Solutions for Second-order Impulsive Differential Equations on the Half-line [J].

Dai, Binxiang ;

Zhang, Dan .

RESULTS IN MATHEMATICS, 2013, 63 (1-2) :135-149

[6]

Hernández E, 2013, P AM MATH SOC, V141, P1641

[7] Variational formulation of a damped Dirichlet impulsive problem [J].

Nieto, Juan J. .

APPLIED MATHEMATICS LETTERS, 2010, 23 (08) :940-942

[8] Variational approach to impulsive differential equations [J].

Nieto, Juan J. ;

O'Regan, Donal .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (02) :680-690

[9]

Pierri M., 2015, MEDITERR J MATH, P1

[10] Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses [J].

Pierri, Michelle ;

O'Regan, Donal ;

Rolnik, Vanessa .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (12) :6743-6749

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