Ordinary differential equations with delta function terms
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Publication:5259322
DOI10.2298/PIM1205125NzbMath1452.46030MaRDI QIDQ5259322
Marko Nedeljkov, Michael Oberguggenberger
Publication date: 26 June 2015
Published in: Publications de l'Institut Math?matique (Belgrade) (Search for Journal in Brave)
Nonlinear ordinary differential equations and systems (34A34) Operations with distributions and generalized functions (46F10)
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Describing limits of integrable functions as grid functions of nonstandard analysis ⋮ Strong solutions of a semilinear impulsive pseudoparabolic equation with an infinitesimal initial layer ⋮ Analytical solutions of linear delay-differential equations with Dirac delta function inputs using the Laplace transform ⋮ Weak solutions of impulsive pseudoparabolic equations with an infinitesimal transition layer ⋮ Dirac delta-function in optimal control of age-structured populations ⋮ Grid functions of nonstandard analysis in the theory of distributions and in partial differential equations ⋮ Nonlinear stochastic differential equations containing generalized delta processes ⋮ Extension of Colombeau algebra to derivatives of arbitrary order D\(^\alpha ,\alpha \in \mathbf R_+ \cup \{0\}\). Application to ODEs and PDEs with entire and fractional derivatives ⋮ On the interpretation of Dirac δ pulses in differential equations for phase oscillators ⋮ The impulsive heat equation with the Volterra transition layer ⋮ Strong solutions of impulsive pseudoparabolic equations
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