The perturbed Klein-Gordon equation


We establish a general existence reasults for the Klein-Gordon equation with multivalued perturbations. The approach is based on a new fixed point theorem  given in [10].


Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Hyperbolic equation; Differential inclusion; Nonlinear operator.

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R. Precup, The perturbed Klein-Gordon equation, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, 1 (2003), 141-152.


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[1] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei-Noordhoff International Publishing, Bucuresti-Leyden, 1976.
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[3] J.F. Couchourou and R. Precup, Existence principles for inclusions of Hammerstein type involving noncompact acyclic multivalued maps, Electron. J. Differential Equations 2002 )2002), no.4, 1-21.
[4] J.F. Couchouron and R. Precup, Anti-periodic solutions for second order differential inclusions, to appear.
[5] M. Kamenskii, V. Obukhovski and P. Zecca, Condensing Multivalued Maps and Semiliniear Differential Inclusions in Banach Spaces, Walter de Gruyter, Berlin-New York, 2001.
[6] J.L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Dunod et Gauthier-Villars, Paris, 1969.
[7] D.O’Regan and R. Precup, Fixed point theorems for set-valued maps and existence principles forintegral inclusions, J. Math. Anal. Appl. 245 (2000), 594-612.
[8]  D. O’Regan and R. Precup, Existence theory for nonlinear operator equations of Hammerstein type in Banach spaces, J. Dynamics Systems Appl.., to appear
[9] R. Precup, Partial Differential Equations (Romanian), Transilvania Press, Cluj, 1997.
[10] R. Precup, Fixed point theorems for decomposable multivalued maps and applications, to appear.


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