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Orbitally stable standing waves for the asymptotically linear onedimensional NLS
Analyticity and regularity for a class of second order evolution equations
1.  Laboratoire JacquesLouis Lions, U.M.R C.N.R.S. 7598, Université Pierre et Marie Curie, Boite courrier 187, 75252 Paris Cedex 05, France 
2.  Department of Applied Physics, School of Science and Engineering, Waseda University, 341, Okubo, Shinjukuku, Tokyo, 1698555, Japan 
References:
[1] 
T. Cazenave and A. Haraux, "An Introduction to Semilinear Evolution Equations," Oxford Lecture Series in Mathematics and its Applications, 13, 1998. 
[2] 
G. Chen and D. L. Russell, A mathematical model for linear elastic systems with structural damping,, Quart. Appl. Math., 39 (): 433. 
[3] 
S. Chen and R. Triggiani, Proof of extension of two conjectures on structural damping for elastic systems: The case $\frac{1}{2} \le\alpha\le 1$, Pacific. J. Math., 136 (1989), 1555. 
[4] 
S. Chen and R. Triggiani, Gevrey class semigroups arising from elastic systems. The case $\alpha \in (0, \frac{1}{2})$, Proc. American Math. Soc., 110 (1989), 401405. doi: 10.2307/2048084. 
[5] 
U. Frisch, "Wave Propagation in Random Media, Probabilistic Methods in Applied Mathematics," I, 75198, Academic press, NewYork 1968. 
[6] 
K. Masuda, Manuscript for seminar at Kyoto University,, 1970., (). 
[7] 
M. Ôtani, $L^\infty$energy method and its applications, in "Nonlinear Partial Differential Equations and Their Applications" (Ed. by N. Kenmochi, M. Ôtani and S. Zheng ), GAKUTO Internat. Ser. Math. Sci. Appl., 20, Gakkotosho, Tokyo, (2004), 505516. 
[8] 
M. Ôtani, $L^\infty$energy method, basic tools and usage, in "Differential Equations, Chaos and Variational Problems: Progress in Nonlinear Differential Equations and Their Applications" (Ed. by Vasile Staicu), 75, Birkhauser (2007), 357376. doi: 10.1007/9783764384821_27. 
[9] 
A. Pazy, "SemiGroups of Linear Operators and Applications to PDE," Applied Mathematical Science 44, Springer 1983. 
[10] 
H. B. Stewart, Generation of analytic semigroups by strongly elliptic operators, Trans.A.M.S., 199 (1974), 141162. 
show all references
References:
[1] 
T. Cazenave and A. Haraux, "An Introduction to Semilinear Evolution Equations," Oxford Lecture Series in Mathematics and its Applications, 13, 1998. 
[2] 
G. Chen and D. L. Russell, A mathematical model for linear elastic systems with structural damping,, Quart. Appl. Math., 39 (): 433. 
[3] 
S. Chen and R. Triggiani, Proof of extension of two conjectures on structural damping for elastic systems: The case $\frac{1}{2} \le\alpha\le 1$, Pacific. J. Math., 136 (1989), 1555. 
[4] 
S. Chen and R. Triggiani, Gevrey class semigroups arising from elastic systems. The case $\alpha \in (0, \frac{1}{2})$, Proc. American Math. Soc., 110 (1989), 401405. doi: 10.2307/2048084. 
[5] 
U. Frisch, "Wave Propagation in Random Media, Probabilistic Methods in Applied Mathematics," I, 75198, Academic press, NewYork 1968. 
[6] 
K. Masuda, Manuscript for seminar at Kyoto University,, 1970., (). 
[7] 
M. Ôtani, $L^\infty$energy method and its applications, in "Nonlinear Partial Differential Equations and Their Applications" (Ed. by N. Kenmochi, M. Ôtani and S. Zheng ), GAKUTO Internat. Ser. Math. Sci. Appl., 20, Gakkotosho, Tokyo, (2004), 505516. 
[8] 
M. Ôtani, $L^\infty$energy method, basic tools and usage, in "Differential Equations, Chaos and Variational Problems: Progress in Nonlinear Differential Equations and Their Applications" (Ed. by Vasile Staicu), 75, Birkhauser (2007), 357376. doi: 10.1007/9783764384821_27. 
[9] 
A. Pazy, "SemiGroups of Linear Operators and Applications to PDE," Applied Mathematical Science 44, Springer 1983. 
[10] 
H. B. Stewart, Generation of analytic semigroups by strongly elliptic operators, Trans.A.M.S., 199 (1974), 141162. 
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