On the Existence of Solutions for Abstract Nonlinear Operator Equations

Marek Galewski

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 1089-1100
  • ISSN: 0392-4033

Abstract

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We provide a duality theory and existence results for a operator equation T ( x ) = N ( x ) where T is not necessarily a monotone operator. We use the abstract version of the so called dual variational method. The solution is obtained as a limit of a minimizng sequence whose existence and convergence is proved.

How to cite

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Galewski, Marek. "On the Existence of Solutions for Abstract Nonlinear Operator Equations." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 1089-1100. <http://eudml.org/doc/290416>.

@article{Galewski2007,
abstract = { We provide a duality theory and existence results for a operator equation $\nabla T(x) = \nabla N(x)$ where $T$ is not necessarily a monotone operator. We use the abstract version of the so called dual variational method. The solution is obtained as a limit of a minimizng sequence whose existence and convergence is proved.},
author = {Galewski, Marek},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {1089-1100},
publisher = {Unione Matematica Italiana},
title = {On the Existence of Solutions for Abstract Nonlinear Operator Equations},
url = {http://eudml.org/doc/290416},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Galewski, Marek
TI - On the Existence of Solutions for Abstract Nonlinear Operator Equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 1089
EP - 1100
AB - We provide a duality theory and existence results for a operator equation $\nabla T(x) = \nabla N(x)$ where $T$ is not necessarily a monotone operator. We use the abstract version of the so called dual variational method. The solution is obtained as a limit of a minimizng sequence whose existence and convergence is proved.
LA - eng
UR - http://eudml.org/doc/290416
ER -

References

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  6. KATO, T., Perturbation Theory for Linear Operators, Springer Verlag, 1980. Zbl0435.47001MR203473
  7. MAWHIN, J., Problems de Dirichlet variationnels non lineaires, Les Presses de l'Universite de Montreal, 1987. MR906453
  8. MAWHIN, J. - WILLEM, M., Critical Point Theory, Springer-Verlag, New York, 1989. Zbl0676.58017
  9. NOWAKOWSKI, A., A New Variational Principle and Duality for Periodic Solutions of Hamilton's Equations, J. Differential Equations, vol. 97, No. 1 (1992), 174-188. Zbl0759.34039MR1161317DOI10.1016/0022-0396(92)90089-6
  10. NOWAKOWSKI, A. - ROGOWSKI, A., On the new variational principles and duality for periodic solutions of Lagrange equations with superlinear nonlinearities, J. Math. Analysis App., 264 (2001), 168-181. Zbl0998.34033MR1868335DOI10.1006/jmaa.2001.7667
  11. SMART, D. R., Fixed Point Theorems, Cambridge University Press, 1974. Zbl0297.47042MR467717

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