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Blow-up for a non-local diffusion equation with exponential reaction term and Neumann boundary condition
Free vibrations in space of the single mode for the Kirchhoff string
1. | Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy |
References:
[1] |
M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables," Chapters 16, 17,, New York: Dover, (1964).
|
[2] |
L. P. Bonorino, E. H. M. Brietzke, J. P. Lukaszczyk and C. A. Taschetto, Properties of the period function for some Hamiltonian systems and homogeneous solutions of a semilinear elliptic equation,, J. Differential Equations, 214 (2005), 156.
doi: 10.1016/j.jde.2004.08.007. |
[3] |
G. F. Carrier, On the non-linear vibration problem of an elastic string,, Q. Appl. Math., 3 (1945), 157.
|
[4] |
T. Cazenave and F. B. Weissler, Unstable simple modes of the nonlinear string,, Q. Appl. Math., 54 (1996), 287.
|
[5] |
C. Chicone, The monotonicity of the period function for planar Hamiltonian vector fields,, J. Differential Equations, 69 (1987), 310.
doi: 10.1016/0022-0396(87)90122-7. |
[6] |
C. Chicone, "Ordinary Differential Equations with Applications,", Springer-Verlag, (2006).
|
[7] |
A. Cima, A. Gasull and F. Mañosas, Period function for a class of Hamiltonian systems,, J. Differential Equations, 168 (2000), 180.
doi: 10.1006/jdeq.2000.3912. |
[8] |
W. R. Dean, Note on the evaluation of an elliptic integral of the third kind,, J. London Math. Soc., 18 (1943), 130.
doi: 10.1112/jlms/s1-18.3.130. |
[9] |
R. W. Dickey, Stability of periodic solutions of the non linear string,, Q. Appl. Math., 38 (): 253.
|
[10] |
G. Gallavotti, "The Elements of Mechanics,", Springer-Verlag, (1983).
|
[11] |
M. Ghisi and M. Gobbino, Stability of simple modes of the Kirchhoff equation,, Nonlinearity, 14 (2001), 1197.
doi: 10.1088/0951-7715/14/5/314. |
show all references
References:
[1] |
M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables," Chapters 16, 17,, New York: Dover, (1964).
|
[2] |
L. P. Bonorino, E. H. M. Brietzke, J. P. Lukaszczyk and C. A. Taschetto, Properties of the period function for some Hamiltonian systems and homogeneous solutions of a semilinear elliptic equation,, J. Differential Equations, 214 (2005), 156.
doi: 10.1016/j.jde.2004.08.007. |
[3] |
G. F. Carrier, On the non-linear vibration problem of an elastic string,, Q. Appl. Math., 3 (1945), 157.
|
[4] |
T. Cazenave and F. B. Weissler, Unstable simple modes of the nonlinear string,, Q. Appl. Math., 54 (1996), 287.
|
[5] |
C. Chicone, The monotonicity of the period function for planar Hamiltonian vector fields,, J. Differential Equations, 69 (1987), 310.
doi: 10.1016/0022-0396(87)90122-7. |
[6] |
C. Chicone, "Ordinary Differential Equations with Applications,", Springer-Verlag, (2006).
|
[7] |
A. Cima, A. Gasull and F. Mañosas, Period function for a class of Hamiltonian systems,, J. Differential Equations, 168 (2000), 180.
doi: 10.1006/jdeq.2000.3912. |
[8] |
W. R. Dean, Note on the evaluation of an elliptic integral of the third kind,, J. London Math. Soc., 18 (1943), 130.
doi: 10.1112/jlms/s1-18.3.130. |
[9] |
R. W. Dickey, Stability of periodic solutions of the non linear string,, Q. Appl. Math., 38 (): 253.
|
[10] |
G. Gallavotti, "The Elements of Mechanics,", Springer-Verlag, (1983).
|
[11] |
M. Ghisi and M. Gobbino, Stability of simple modes of the Kirchhoff equation,, Nonlinearity, 14 (2001), 1197.
doi: 10.1088/0951-7715/14/5/314. |
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