Variational approach to differential equations with not instantaneous impulses. (November 2017)

• Record Type: Journal Article
• Authors: Bai, Liang; Nieto, Juan J.
• Is Part Of: Applied mathematics letters. Volume 73(2017:Nov.)
• Page Start: 44
• Page End: 48
• Publication Date: 2017-11
• Subjects: Non-instantaneous impulse -- Variational method -- Lax–Milgram theorem -- Critical point -- Impulsive differential equation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2017.02.019
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.