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Applicable Analysis
An International Journal
Volume 69, 1998 - Issue 1-2
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Original Articles

Global solutions to kirchhoff equations with non-local nonlinearities defined by a potential

Pages 1155-1168 | Published online: 02 May 2007

  • Arosio , A. and Spagnolo , S. 1984 . S., Global solution to the Cauchy problem for a nonlinear equation, in Nonlinear PDE's and their applications, . College de France Seminar, . 1984 , Pitman, Boston,. Research Notes Math. . H. Brezis and J.L. Lions (eds.), Vol. VI, 1–26 109
  • Bernstein , S. 1940 . Sur une classe d18quations fonctionelles aux dérivées partielles, . Izv. Akad. Nauk SSSR, Sér Math. , 4 : 17 – 26 .
  • Callegari , E. and Manfrin , R. 1996 . Global existence for non-linear hyperbolic systems of Kirchhoff type, . Jour. of Diff. Equatzons , 132 : 239 – 274 .
  • Callegari E. Manfrin R. Global small solutions to Klein-Gordon type equations with non-local nonlinearities to appear.
  • Carrier , G.F. 1945 . On the nonlinear vibration problem of the elastic string, . Quart. Appl. Math. , 3 : 157 – 165 .
  • D'ancona , P. and Spangnolo , P. 1993 . A Class of Nonlinear Hyperbolic Problems with Global Solutions, . Arch. Rat. Mech. Analysis , 124 : 201 – 219 .
  • Spangnolo , S. 1994 . Nonlinear perturbations of the Kirchhoff equation, . Comm. Pun Appl. Math. , 47 : 1005 – 1029 .
  • Spangnolo , S. 1992 . “ On an abstract weakly hyperbolic equation modelling the nonlinear vibrating string, ” . In "Developments in PDEs and Applications to Mathematical Physics" , Edited by: Spangnolo , S. Buttazzo : Plenum Press . G. and Galdi, G.P. eds., in
  • D'Ancona P. Spagnolo S. Kirchhoff type equations depending on a small parameter to appear in Chinese Ann. Math. to appear
  • Dickey , R.W. 1969 . Infinite systems of nonlinear oscillation equations related to the string, . Proc. Am. Math. Soc. , 23 : 459 – 468 .
  • Dickey , R.W. 1970 . Infinite systems of nonlinear oscillation equations with linear damping, . SIAM J. Appl. Math. , 19 : 208 – 214 .
  • Greenberg , J.M. and Hu , S.C. 1980 . The initial value problem for a stretched string, . Quai. Appl. Math. , 38 : 289 – 311 .
  • Kirchhoff G. Vorlesungen öber Mechanik Teubner Leipzig 1883
  • Manfrin , R. 1997 . On the global solvability of symmetric hyperbolic syslems of Kirchhoff type, . Discr. and Cont. Dynamical Systems , 3 : 91 – 106 .
  • Madeiros , L.A. and Mirinda , M. 1987 . Solutions for the equation of nonlinear vibrations in Sobolev spaces of fractionary order, . Computational Applied Math. , 6 : 257 – 267 .
  • Nishihara , K. 1984 . On a global solution of some quasilinear hyperbolic equation, . Tokyo J. Math. , 7 : 437 – 459 .
  • Perla Menzala , G. 1979 . On classical solutions of a quasilinear hyperbolic equation, . Nonlinear Analysts , 3 : 613 – 627 .
  • Pohoöaev , S.I. 1975 . Mat. Sbornik , 96 ( 138 ) : 152 – 166 . [Transl. : Math. USSR Sbornik 25 (1975) N.11
  • Racke , R. 1995 . Generalized Fourier transform and global, small solutions to Kircbhoff equations, . Appl. Analysis Vol. , 58 : 85 – 100 .
  • Rivera Rodriguez , R.H. 1980 . On local strong solutions of a non-linear partial differential equation, . Appl. Anal. , 8 : 93 – 104 .
  • Sogge , C.D. 1993 . “ Fourier Integrals in Classical Analysis, ” . cambridge, New York : Cambridge Univ. Press, .
  • Spangnolo , S. 1992 . The Cauchy problem for the Kirchhoff equations, . Rend. Sem. Fisico Matematico di Milano , 62 : 17 – 51 .
  • Yarnada , Y. 1987 . Some nonlinear degenerate wave equations, . Nonlinear Analysis , 11 ( 10 ) : 1155 – 1168 .

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