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Zbl 1197.34041
Nieto, Juan J.
Variational formulation of a damped Dirichlet impulsive problem. (English)
[J] Appl. Math. Lett. 23, No. 8, 940-942 (2010). ISSN 0893-9659

Summary: 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.

MSC 2000:: *34B37 Boundary value problems with impulses
58E30 Variational principles on infinite-dimensional spaces

Keywords: Lax-Milgram theorem; variational formulation; critical point; Dirichlet boundary condition; impulsive differential equation

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Zentralblatt MATH Berlin [Germany]