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A class of nonlinear hyperbolic problems with global solutions

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References

  1. Arosio, A. &Spagnolo, S., Global solution to the Cauchy problem for a nonlinear equation, inNonlinear PDE's and their applications, Collège de France Seminar,H. Brezis &J. L. Lions (eds.), Vol. VI, Research Notes Math.109, Pitman (1984), 1–26.

  2. Ball, J. M., Saddle point analysis for an ordinary differential equation in a Banach space and an application to dynamic buckling of a beam, inNonlinear Elasticity,R. W. Dickey (ed.), Academic Press (1973), 93–160.

  3. Bernstein, S., Sur une classe d'équations fonctionnelles aux dérivées partielles,Izv. Akad. Nauk SSSR, Sér. Math.4 (1940), 17–26.

    Google Scholar 

  4. Carrier, G. F., On the nonlinear vibration problem of the elastic string,Quart. Appl. Math. 3 (1945), 157–165.

    Google Scholar 

  5. Cazenave, T., Haraux, A. &Weissler, F. B., Une équation des ondes complètement intégrable avec non-linéarité homogène de degré trois,C. Rend. Acad. Paris 313 (1991), 237–241.

    Google Scholar 

  6. Cazenave, T., Haraux, A. &Weissler, F. B., A class on nonlinear completely integrable abstract wave equations,Publ. Lab. Anal. Num. Paris VI (1992).

  7. Dickey, R. W., Infinite systems of nonlinear oscillation equations related to the string,Proc. Am. Math. Soc. 23 (1969), 459–468.

    Google Scholar 

  8. Dickey, R. W., Infinite systems of nonlinear oscillation equations with linear damping,SIAM J. Appl. Math. 19 (1970), 208–214.

    Google Scholar 

  9. D'ancona, P. &Spagnolo, S., Global solvability for the degenerate Kirchhoff equation with real analytic data,Invent. Math. 108 (1992), 247–262.

    Google Scholar 

  10. Grothendieck, A.,Topological vector spaces, Gordon and Breach (1973).

  11. Greenberg, J. M. &Hu, S. C., The initial value problem for a stretched string,Quart. Appl. Math. (1980), 289–311.

  12. Kirchhoff, G.,Vorlesungen über Mechanik, Teubner (1883).

  13. Medeiros, L. A., On a new class of nonlinear wave equations,J. Math. Anal. Appl. 69 (1979), 252–262.

    Google Scholar 

  14. Narasimha, R., Nonlinear vibrations of an elastic string,J. Sound Vibrations 8 (1968), 134–146.

    Google Scholar 

  15. Nishida, T., A note on the nonlinear vibrations of the elastic string,Mem. Fac. Engng. Kyoto Univ. 33 (1971), 329–341.

    Google Scholar 

  16. Perla Menzala, G., On classical solutions of a quasilinear hyperbolic equation,Nonlinear Anal. 3 (1979), 613–627.

    Google Scholar 

  17. Pohožaev, S. I., On a class of quasilinear hyperbolic equations,Mat. Sbornik. 96 (1975), 152–166 [Transl:Math. USSR Sbornik 25 (1975), 145–158].

    Google Scholar 

  18. Rivera Rodriguez, P. H., On local strong solution of a non-linear partial differential equation,Appl. Anal. 8 (1980), 93–104.

    Google Scholar 

  19. Yamanda, Y., On some quasilinear wave equations with dissipative terms,Nagoya Math. J. 87 (1982), 17–39.

    Google Scholar 

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D'Ancona, P., Spagnolo, S. A class of nonlinear hyperbolic problems with global solutions. Arch. Rational Mech. Anal. 124, 201–219 (1993). https://doi.org/10.1007/BF00953066

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