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On variational principles for nonlinear partial differential equations in complex spaces

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Il Nuovo Cimento B (1971-1996)

Summary

The necessary and sufficient conditions for an abstract equation in a complex Banach space to admit a variational principle, which one of us described in a previous paper, are here applied to a system of nonlinear partial differential equations of arbitrary order in a complexL 2 space. More specific and helpful conditions are thus obtained. General consequences and special implications for some classes of nonlinear Schröndinger equations are also discussed and differences from an analogous result valid only in real spaces are put in evidence.

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Authors and Affiliations

  1. Scuola Internazionale Superiore di Studi Avanzati (SISSA), Strada Costiera 11, 34014, Trieste, Italia

    A. E. Borzí

  2. Dipartimento di Fisica dell’Università, Corso Italia 57, 95129, Catania, Italia

    G. Fonte

Authors
  1. A. E. Borzí
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  2. G. Fonte
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Work supported by M.U.R.S.T.

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Borzí, A.E., Fonte, G. On variational principles for nonlinear partial differential equations in complex spaces. Nuov Cim B 107, 189–201 (1992). https://doi.org/10.1007/BF02722916

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  • DOI: https://doi.org/10.1007/BF02722916

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