# American Institute of Mathematical Sciences

January & February  2004, 10(1&2): 497-505. doi: 10.3934/dcds.2004.10.497

## On the over determinedness of some functional equations

 1 Department of Mathematics, Technion, Haifa, 32000, Israel

Received  December 2002 Revised  May 2003 Published  October 2003

It is shown that some well known functional equations in $\mathbb R^n, n\geq 2$, turn out to be overdetermined. This means that their solutions are uniquely defined if the corresponding relations are fulfilled not in the whole spaces $\mathbb R^n, n\geq 2$, but only at the points of some smooth submanifolds in $\mathbb R^n$.
Citation: Boris Paneah. On the over determinedness of some functional equations. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 497-505. doi: 10.3934/dcds.2004.10.497
 [1] Venkatesan Govindaraj, Raju K. George. Controllability of fractional dynamical systems: A functional analytic approach. Mathematical Control & Related Fields, 2017, 7 (4) : 537-562. doi: 10.3934/mcrf.2017020 [2] Daniel Franco, J. R. L. Webb. Collisionless orbits of singular and nonsingular dynamical systems. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 747-757. doi: 10.3934/dcds.2006.15.747 [3] Chao Ma, Baowei Wang, Jun Wu. Diophantine approximation of the orbits in topological dynamical systems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2455-2471. doi: 10.3934/dcds.2019104 [4] Chen-Chang Peng, Kuan-Ju Chen. Existence of transversal homoclinic orbits in higher dimensional discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1181-1197. doi: 10.3934/dcdsb.2010.14.1181 [5] Armengol Gasull, Víctor Mañosa. Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 651-670. doi: 10.3934/dcdsb.2019259 [6] Ismael Maroto, Carmen NÚÑez, Rafael Obaya. Dynamical properties of nonautonomous functional differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3939-3961. doi: 10.3934/dcds.2017167 [7] Mostafa Abounouh, H. Al Moatassime, J. P. Chehab, S. Dumont, Olivier Goubet. Discrete Schrödinger equations and dissipative dynamical systems. Communications on Pure & Applied Analysis, 2008, 7 (2) : 211-227. doi: 10.3934/cpaa.2008.7.211 [8] Tomás Caraballo, Francisco Morillas, José Valero. On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems. Discrete & Continuous Dynamical Systems - A, 2014, 34 (1) : 51-77. doi: 10.3934/dcds.2014.34.51 [9] Bin Wang, Arieh Iserles. Dirichlet series for dynamical systems of first-order ordinary differential equations. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 281-298. doi: 10.3934/dcdsb.2014.19.281 [10] Fabio Ancona, Andrea Marson. On the Glimm Functional for general hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 44-53. doi: 10.3934/proc.2011.2011.44 [11] Alain Jacquemard, Weber Flávio Pereira. On periodic orbits of polynomial relay systems. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 331-347. doi: 10.3934/dcds.2007.17.331 [12] Tomás Caraballo, Gábor Kiss. Attractivity for neutral functional differential equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1793-1804. doi: 10.3934/dcdsb.2013.18.1793 [13] El Houcein El Abdalaoui, Sylvain Bonnot, Ali Messaoudi, Olivier Sester. On the Fibonacci complex dynamical systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2449-2471. doi: 10.3934/dcds.2016.36.2449 [14] Lianfa He, Hongwen Zheng, Yujun Zhu. Shadowing in random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 355-362. doi: 10.3934/dcds.2005.12.355 [15] Fritz Colonius, Marco Spadini. Fundamental semigroups for dynamical systems. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 447-463. doi: 10.3934/dcds.2006.14.447 [16] John Erik Fornæss. Sustainable dynamical systems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1361-1386. doi: 10.3934/dcds.2003.9.1361 [17] Vieri Benci, C. Bonanno, Stefano Galatolo, G. Menconi, M. Virgilio. Dynamical systems and computable information. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 935-960. doi: 10.3934/dcdsb.2004.4.935 [18] Mădălina Roxana Buneci. Morphisms of discrete dynamical systems. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 91-107. doi: 10.3934/dcds.2011.29.91 [19] Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 1-16. doi: 10.3934/dcds.2011.30.1 [20] Tobias Wichtrey. Harmonic limits of dynamical systems. Conference Publications, 2011, 2011 (Special) : 1432-1439. doi: 10.3934/proc.2011.2011.1432

2018 Impact Factor: 1.143