References
A. Arosio and S. Spagnolo, Global Solutions of the Cauchy Problem for a Nonlinear Hyperbolic Equation. Università di Pisa, Dipartimento di Mathematica (Roma, 1982).
I. N. Bernstein, Sur une classe d'équations fonctionelles aux derivées partielles, Izv. Akad. Nauk SSSR Ser. Math., 4 (1940), 17–26.
R. W. Dickey, Infinite systems of nonlinear oscillations equations related to the string, Proc. Amer. Math. Soc., 23 (1969), 459–468.
Y. Ebihara, On solutions of semilinear wave equations, Nonlinear Analysis, 6 (1982), 467–486.
Y. Ebihara, L. A. Medeiros and M. Milla Miranda, Local solutions for a nonlinear degenerate hyperbolic equation, Nonlinear Analysis, Theory, Methods and Appl., 10 (1986), 27–40.
J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Lineaires, Dunod (Paris, 1969).
J. L. Lions, On Some Questions in Boundary Value Problems of Mathematical Physics, North Holland, Mathematical Studies 30 (1978), Editors G. de La Penha and L. A. Medeiros.
A. H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover (New York, 1944).
D. C. Pereira and R. M. Izaguirre, Sobre uma equação de vibrações não lineares, Proceedings of 23° Seminário Brasileiro de Análise (Campinas, São Paulo, 1986), 155–158.
D. C. Pereira, Problema misto para uma equação de vibrações não lineares, Revista Paranaense de Matemática, 9 (1988), 31–42.
D. C. Pereira and Y. Ebihara, On a global classical solution of a quasilinear hyperbolic equation, Internat. J. Math. & Math. Sci., 12 (1989), 29–38.
S. I. Pohozaev, On a class of quasilinear hyperbolic equations, Mat. USSR Sbornik, 25 (1975), 145–158.
Y. Yamada, Some nonlinear degenerate wave equation, Nonlinear Analysis, Theory, Methods and Applications, 11 (1987), 1155–1168.
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Pereira, D.C., De Campos Vieira, M.C. & Rabello, T.N. Local solution of a mixed problem for a degenerated hyperbolic equation. Acta Math Hung 60, 61–71 (1992). https://doi.org/10.1007/BF00051757
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DOI: https://doi.org/10.1007/BF00051757