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Zbl 1167.34318
Nieto, Juan J.; O'Regan, Donal
Variational approach to impulsive differential equations. (English)
[J] Nonlinear Anal., Real World Appl. 10, No. 2, 680-690 (2009). ISSN 1468-1218

Summary: Many dynamical systems have an impulsive dynamical behavior due to abrupt changes at certain instants during the evolution process. The mathematical description of these phenomena leads to impulsive differential equations.In this work we present a new approach via variational methods and critical point theory to obtain the existence of solutions to impulsive problems.We consider a linear Dirichlet problem and the solutions are found as critical points of a functional. We also study the nonlinear Dirichlet impulsive problem.

MSC 2000:: *34B37 Boundary value problems with impulses
47J30 Variational methods

Keywords: impulsive ordinary differential equations; Lax-milgram theorem; critical points; mountain pass theorem; Dirichlet boundary conditions

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Zentralblatt MATH Berlin [Germany]