A unified variational approach to discontinuous differential equations


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.


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

Jorge Rodríguez-López
Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782, Facultade de Matemáticas, Campus Vida, Santiago, Spain



Nonsmooth critical point theory; Discontinuous differential equation; Multivalued operator

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R. Precup, J. Rodríguez-López, A unified variational approach to discontinuous differential equations, Mediterr. J. Math. 18 (2021) art. no. 62, 14 pp., https://doi.org/10.1007/s00009-021-01705-9



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Mediterranean Journal of Mathematics

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