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On the existence of weak solutions for a nonlinear time dependent Dirac equation*

  • João-Paulo Dias (a1) and Mário Figueira (a1)


In this paper we prove the existence of a weak solution of the Cauchy problem for the nonlinear Dirac equation in ℝ × ℝ

where X(r) is the characteristic function of a compact interval of ]0, + ∞[



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1Bjorken, J. D. and Drell, S. D.. Relativistic Quantum Mechanics (New York: McGraw-Hill, 1964).
2Cazenave, T. and Weissler, F.. The Cauchy problem for the nonlinear Schrödinger equation in H1. Manuscripta Math. 61 (1988), 477494.
3Dias, J. P. and Figueira, M.. Sur l'existence d'une solution globale pour une équation de Dirac non linéaire avec masse nulle. C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), 469472.
4Dias, J. P. and Figueira, M.. Remarque sur le problème de Cauchy pour une équation de Dirac non linéaire avec masse nulle. Portugal. Math. 45 (1988), 327335.
5Lions, J. L.. Quelques méthodes de résolution des problèmes aux limites non linéaires (Paris: Dunod, 1969).
6Reed, M.. Abstract Non-linear Wave Equations. Lecture Notes in Mathematics 507 (Berlin: Springer, 1976).
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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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