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Non Absolute Integration and Applications

Abstract

The main objective of this Project is to continue our research in Non-Absolute Integration theory and in theory of Generalized Ordinary Differential Equations, as well as the applications of these theories to the investigation of properties of the solutions of Ordinary and Functional Differential Equations (with delay or advance) Differential Equations on Time Scales, Impulsive Differential Equations, Measure Differential Equations, Neutral Functional Differential Equations, Integral Equations, and others, whenever the functions involved are very oscillating and hence not Lebesgue integrable.From the point of view of Mathematics, the Project is inserted in the qualitative study of solutions of various types of Differential and Integral Equations by transferring the properties of Generalized Ordinary Differential Equations and/or via applications of the Kurzweil-Henstock integral directly to the models.From the point of view of applications, the Project contributes especially to the development of sectors of the Chemical and Pharmaceutical Sciences (e.g., pharmacokinetics), Engineering (e.g., electrical circuits) and Physics (e.g., quantum mechanics), as well as models involving many jumps and highly oscillating functions. (AU)

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Scientific publications (9)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FEDERSON, M.; FRASSON, M.; MESQUITA, J. G.; TACURI, P. H.. Measure Neutral Functional Differential Equations as Generalized ODEs. Journal of Dynamics and Differential Equations, v. 31, n. 1, p. 207-236, . (17/13795-2)
FEDERSON, M.; MAWHIN, J.; MESQUITA, C.. Existence of periodic solutions and bifurcation points for generalized ordinary differential equations. BULLETIN DES SCIENCES MATHEMATIQUES, v. 169, . (17/13795-2)
BONOTTO, E. M.; FEDERSON, M.; SANTOS, F. L.. Robustness of Exponential Dichotomies for Generalized Ordinary Differential Equations. Journal of Dynamics and Differential Equations, v. 32, n. 4, . (16/24711-1, 11/24027-0, 17/13795-2)
FEDERSON, M.; GYORI, I; MESQUITA, J. G.; TABOAS, P.. A Delay Differential Equation with an Impulsive Self-Support Condition. Journal of Dynamics and Differential Equations, v. 32, n. 2, p. 605-614, . (13/17104-3, 17/13795-2, 14/04732-9)
BONOTTO, E. M.; FEDERSON, M.; GADOTTI, M. C.. Recursive properties of generalized ordinary differential equations and applications. Journal of Differential Equations, v. 303, p. 123-155, . (17/13795-2, 19/03188-7)
DA SILVA, F. ANDRADE; FEDERSON, M.; GRAU, R.; TOON, E.. Converse Lyapunov theorems for measure functional differential equations. Journal of Differential Equations, v. 286, p. 46-pg., . (17/13795-2)
DA SILVA, F. ANDRADE; FEDERSON, M.; TOON, E.. Stability, boundedness and controllability of solutions of measure functional differential equations. Journal of Differential Equations, v. 307, p. 160-210, . (17/13795-2)
FEDERSON, MARCIA; GRAU, ROGELIO; MESQUITA, CAROLINA. AFFINE-PERIODIC SOLUTIONS FOR GENERALIZED ODES AND OTHER EQUATIONS. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 60, n. 2, p. 36-pg., . (17/13795-2)

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