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On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points
1. | Department of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland, Poland |
References:
[1] |
J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, 1990. |
[2] |
D. Bors, A. Skowron and S. Walczak, Optimal control and stability of elliptic systems with integral cost functional, Systems Science, 33 (2007), 13-26. |
[3] |
D. Bors and S. Walczak, Nonlinear elliptic systems with variable boundary data, Nonlinear Analysis: Theory, Methods and Applications, 52 (2003), 1347-1364.
doi: 10.1016/S0362-546X(02)00179-7. |
[4] |
L. Bourdin, Existence of a weak solution for fractional Euler-Lagrange equations, Journal of Mathematical Analysis and Applications, 399 (2013), 239-251.
doi: 10.1016/j.jmaa.2012.10.008. |
[5] |
L. Debnath, Recent applications of fractional calculus to science and engineering, International Journal of Mathematics and Mathematical Sciences, 54 (2003), 3413-3442.
doi: 10.1155/S0161171203301486. |
[6] |
D. Idczak, Fractional du Bois-Reymond Lemma of Order $\alpha\in(1/2,1)$, Proceedings of the 7th International Workshop on Multidimensional (nD) Systems (nDs), 2011, Poitiers, France. |
[7] |
R. Kamocki and M. Majewski, On a fractional Dirichlet problem, Proceedings of 17th International Conference Methods and Models in Automation and Robotics (MMAR), (2012), 60-63.
doi: 10.1109/MMAR.2012.6347911. |
[8] |
A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. |
[9] |
L. Nirenberg, Topics in Nonlinear Functional Analysis, New York University - Courant Institute of Mathematical Sciences - AMS, New York, 1974. |
[10] |
I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Vol. 198, Academic Press, California, 1999. |
[11] |
S. Walczak, On the continuous dependance on parameters of solutions of the Dirichlet problem: Part I. Coercive case; Part II. The case of saddle points, Bulletin de la Classe des Sciences de l'Académie Royale de Beligique, 6 (1995), 247-261. |
show all references
References:
[1] |
J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, 1990. |
[2] |
D. Bors, A. Skowron and S. Walczak, Optimal control and stability of elliptic systems with integral cost functional, Systems Science, 33 (2007), 13-26. |
[3] |
D. Bors and S. Walczak, Nonlinear elliptic systems with variable boundary data, Nonlinear Analysis: Theory, Methods and Applications, 52 (2003), 1347-1364.
doi: 10.1016/S0362-546X(02)00179-7. |
[4] |
L. Bourdin, Existence of a weak solution for fractional Euler-Lagrange equations, Journal of Mathematical Analysis and Applications, 399 (2013), 239-251.
doi: 10.1016/j.jmaa.2012.10.008. |
[5] |
L. Debnath, Recent applications of fractional calculus to science and engineering, International Journal of Mathematics and Mathematical Sciences, 54 (2003), 3413-3442.
doi: 10.1155/S0161171203301486. |
[6] |
D. Idczak, Fractional du Bois-Reymond Lemma of Order $\alpha\in(1/2,1)$, Proceedings of the 7th International Workshop on Multidimensional (nD) Systems (nDs), 2011, Poitiers, France. |
[7] |
R. Kamocki and M. Majewski, On a fractional Dirichlet problem, Proceedings of 17th International Conference Methods and Models in Automation and Robotics (MMAR), (2012), 60-63.
doi: 10.1109/MMAR.2012.6347911. |
[8] |
A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. |
[9] |
L. Nirenberg, Topics in Nonlinear Functional Analysis, New York University - Courant Institute of Mathematical Sciences - AMS, New York, 1974. |
[10] |
I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Vol. 198, Academic Press, California, 1999. |
[11] |
S. Walczak, On the continuous dependance on parameters of solutions of the Dirichlet problem: Part I. Coercive case; Part II. The case of saddle points, Bulletin de la Classe des Sciences de l'Académie Royale de Beligique, 6 (1995), 247-261. |
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