TOPOLOGICAL STRUCTURAL STABILITY ON PROJECTED SPACES

Authors

  • Rodiak Figueroa
  • German Lozada
  • José Langa
  • Eder Aragao

DOI:

https://doi.org/10.17268/sel.mat.2016.01.06

Keywords:

Stability, projected spaces, Banach spaces

Abstract

In this work we study the topological structural stability for a family of nonlinear semigroups Th(·) on Banach spaces Xh which dependent on a parameter h.

References

Aragao-Costa, E.R.; Caraballo, T.; Carvalho, A.N.; Langa, J.A. Stability of gradient semigroups under perturbations. Nonlinearity, v. 24, n. 7, p. 2099–2117, 2011.

Aragao-Costa, E.R.; Figueroa-López, R.N.; Langa, J.A.; Lozada-Cruz, G. Topological structural stability of partial differential equations on projected spaces. Journal of Dynamics and Differential Equations, accepted 2016.

Arrieta, J.M.; Carvalho, A.N.; Lozada-Cruz, G. J. Dynamics in dumbbell domains I: continuity of the set of equilibria. Journal of Differential Equations, New York, v. 231, n. 2, p. 551–597, 2006.

Arrieta, J. M.; Carvalho, A. N.; Lozada-Cruz, G. J. Dynamics in dumbbell domains II: the limiting problem. Journal of Differential Equations, New York, v. 247, n. 1, p. 174–202, 2009a.

Arrieta, J. M.; Carvalho, A. N.; Lozada-Cruz, G. J. Dynamics in dumbbell domains III: continuity of attractors. Journal of Differential Equations, New York, v. 247, n. 1, p. 225–259, 2009b.

Carvalho, A. N.; Langa, J. A. An extension of the concept of gradient semigroup wich is stable under perturbations.

Journal of Differential Equations, New York, v. 246, n. 7, p. 2646–2668, 2009.

Carvalho, A. N.; Langa, J. A.; Robinson, J. C. Attractors for infinite-dimensional non-autonomous dynamical systems, Applied Mathematical Sciences 182, Springer, New York, 2013.

Carvalho, A. N., Piskarev, S. A general approximations scheme for attractors of abstract parabolic problems. Numerical Functional Analysis and Optimization, New York, v. 27, n. 7/8, p. 785–829, 2006.

Vainikko, G. Approximative methods for nonlinear equations (two approaches to the convergence problem). Nonlinear Analysis, Theory, Methods and Applications, Oxford, v. 2, n. 6, p. 647–687, 1978.

Vainikko, G. Discretely compact sequences. USSR Computational Mathematics and Mathematical Physics, v. 14, n. 3, p. 32–43, 1974.

Vainikko, G. Funktionalanalysis der diskretisierungsmethoden. Leipzig: BSB B. G. Teubner Verlagsgesellschaft, 1976.

Vainikko, G. Multidimensional weakly singular integral equations. Berlin: Springer-Verlag, 1993.

Vainikko, G. Regular convergence of operators and approximate solution of equations. Itogi Nauki i Tehniki:Seriya Matematicheskii Analiz, Moscow, v. 16, p. 5–53, 1979.

Published

2016-11-30

How to Cite

Figueroa, R., Lozada, G., Langa, J., & Aragao, E. (2016). TOPOLOGICAL STRUCTURAL STABILITY ON PROJECTED SPACES. Selecciones Matemáticas, 3(01), 43-46. https://doi.org/10.17268/sel.mat.2016.01.06