# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Variational formulation of a damped Dirichlet impulsive problem. (English) Zbl 1197.34041
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:
 34B37 Boundary value problems for ODE with impulses 58E30 Variational principles on infinite-dimensional spaces
##### References:
 [1] Chipot, M.: Elements of nonlinear analysis, (2000) · Zbl 0964.35002 [2] Lax, P. D.; Milgram, A. N.: L.bersss.bochnerf.johnparabolic equations; in contributions to the theory of partial differential equations, Parabolic equations; in contributions to the theory of partial differential equations, 167-190 (1954) [3] Brattka, V.; Yoshikawa, A.: Towards computability of elliptic boundary value problems in variational formulation, J. complexity 22, 858-880 (2006) · Zbl 1126.03052 · doi:10.1016/j.jco.2006.04.007 [4] Drivaliaris, D.; Yannakalis, N.: Generalizations of the Lax–Milgram theorem, Bound. value probl. 2007 (2007) · Zbl 1140.47303 · doi:10.1155/2007/87104 [5] Nieto, J. J.; O’regan, D.: Variational approach to impulsive differential equations, Nonlinear anal. RWA 10, 680-690 (2009) · Zbl 1167.34318 · doi:10.1016/j.nonrwa.2007.10.022 [6] Mawhin, J.; Willem, M.: Critical point theory and Hamiltonian systems, (1989)