Inclusões Dinâmicas em Escalas Temporais: Existência de Soluções sob a Hipótese de Semicontinuidade Inferior

Authors

  • Geraldo Nunes Silva Universidade Estadual Paulista - UNESP
  • Iguer Luis Domini dos Santos Universidade Estadual Paulista - UNESP
  • Luciano Barbanti UNESP - Universidade Estadual Paulista

DOI:

https://doi.org/10.5540/tema.2012.013.02.0109

Abstract

Neste trabalho consideramos o problema de inclusão diferencial em escalas temporais cujo campo vetorial é uma multifunção, ou seja, uma função que mapea pontos a conjuntos. O trabalho fornece condições de existência sem exigir compacidade do campo vetorial; exige apenas que ele seja convexo, fechado e semicontínuo inferior. Em trabalhos anteriores na literatura, ou o campo é escalar ou exige-se que este, além de convexo, seja compacto e tenha o gráfico fechado.

Author Biography

Geraldo Nunes Silva, Universidade Estadual Paulista - UNESP

string

References

M. Adivar, Y.N. Raffoul, Existence of resolvent for Volterra integral equations on time scales, Bulletin of the Australian Mathematical Society, 82, No.1 (2010), 139-155.

E. Akin-Bohner, Y.N. Raffoul, C.C. Tisdell, Exponential stability in functional dynamic equations on time scales, Communications in Mathematical Analysis, 9, No.1 (2010), 93-108.

E. Akin-Bohner, S. Sun, Existence of solutions for second-order dynamic inclusions, Int. J. Dynamical Systems and Differential Equations, 3, No.1-2 (2011), 24-37.

F.M. Atici, D.C. Biles, First order dynamic inclusions on time scales, Journal of Mathematical Analysis and Applications, 292, No.1 (2004), 222-237.

J. P. Aubin, A. Cellina, "Differential Inclusions", Springer-Verlag, Berlin, 1984.

R. G. Bartle, "The Elements of Integration and Lebesgue Measure", John Wiley and Sons, New York, 1995.

A. Belarbi, M. Benchohra, A. Ouahab, Existence results for impulsive dynamic inclusions on time scales, Electronic Journal of Qualitative Theory of Differential Equations, No. 12 (2005), 22.

M. Bohner, A. Peterson, "Advances in Dynamic Equations on Time Scales", Birkhauser, Boston, 2003.

M. Bohner, A. Peterson, "Dynamic Equations on Time Scales", Birkhauser, Boston, 2001.

M. Bohner, C.C. Tisdell, Second order dynamic inclusions, Journal of Nonlinear Mathematical Physics, 12, No.2 (2005), 36-45.

A. Cabada, D.R. Vivero, Expression of the Lebesgue -integral on time scales as a usual Lebesgue integral; application to the calculus of -antiderivatives, Mathematical and Computer Modelling, 43, No.1-2 (2006), 194-207.

Y. K. Chang, W.T. Li, Existence results for dynamic inclusions on time scales with nonlocal initial conditions, Computers and Mathematics with Applications, 53, No. 1 (2007), 12-20.

L. Erbe, T.S. Hassan, A. Peterson, Oscillation of third order nonlinear functional dynamic equations on time scales, Differential Equations and Dynamical Systems, 18, No.1-2 (2010), 199-227.

H. Gilbert, Existence theorems for first-order equations on time scales with -Caratheódory functions, Advances in Difference Equations, 2010, (2010),1-20.

G.S. Guseinov, Integration on time scales, Journal of Mathematical Analysis and Applications, 285, No.1 (2003), 107-127.

S. Hilger, Analysis on measure chains- a unified approach to continuous and discrete calculus, Results in Mathematics, 18, No.1-2 (1990), 18-56.

E. L. Lima, "Espaços Métricos", Coleção Projeto Euclides, Rio de Janeiro, 2003.

A. Liu, M. Bohner, Gronwall-OuIang-type integral inequalities on time scales, Journal of Inequalities and Applications, 10, (2010), 15.

H. L. Royden, "Real Analysis", Collier-Macmillan Limited, London, 1968.

W. Rudin, "Real and Complex Analysis", third edition, McGraw-Hill Book Company, New York, 1987.

I.L.D. Santos, G.N. Silva, Absolute continuity and existence of solutions to vector dynamic inclusions in time scales, Technical Report, Department of Computing and Statistics, IBILCE, UNESP - Univ Estadual Paulista, São José do Rio Preto, SP, 2011.

Published

2012-04-29

How to Cite

Silva, G. N., dos Santos, I. L. D., & Barbanti, L. (2012). Inclusões Dinâmicas em Escalas Temporais: Existência de Soluções sob a Hipótese de Semicontinuidade Inferior. Trends in Computational and Applied Mathematics, 13(2), 109–120. https://doi.org/10.5540/tema.2012.013.02.0109

Issue

Section

Original Article