A Unified Variational Approach to Discontinuous Differential Equations

• Radu Precup ^[1] ; Jorge Rodríguez López ^[2]
  1. [1] Babeș-Bolyai University

     Babeș-Bolyai University

     Rumanía

     
  2. [2] Universidade de Santiago de Compostela

     Universidade de Santiago de Compostela

     Santiago de Compostela, España

     
• Localización: Mediterranean journal of mathematics, ISSN 1660-5446, Vol. 18, Nº. 2, 2021
• Idioma: inglés
• DOI: 10.1007/s00009-021-01705-9
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• Resumen

  • A direct variational technique involving Clarke generalized gradient is used to treat general boundary value problems with discontinuous nonlinearities. Based on the theory of positive definite symmetric operators it is established the nonsmooth variational form of the regularized inclusions which give the Filippov solutions of the discontinuous problems. These solutions reduce to classical solutions in case that a transversality condition on the set of discontinuities is satisfied. The results apply to a wide class of concrete boundary value problems of different orders. Two illustrative examples are given.