Abstract
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.
Authors
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
Keywords
Nonsmooth critical point theory; Discontinuous differential equation; Multivalued operator
Paper coordinates
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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About this paper
Journal
Mediterranean Journal of Mathematics
Publisher Name
Springer
Print ISSN
1660-5446
Online ISSN
1660-5454
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