A Unified Variational Approach to Discontinuous Differential Equations

被引：0
|
作者：
Radu Precup
Jorge Rodríguez-López
机构：
[1] Babeş-Bolyai University,Department of Mathematics
[2] Instituto de Matemáticas,Departamento de Estatística, Análise Matemática e Optimización
[3] Universidade de Santiago de Compostela,undefined
[4] 15782,undefined
[5] Facultade de Matemáticas,undefined
[6] Campus Vida,undefined
来源：
Mediterranean Journal of Mathematics | 2021年 / 18卷
关键词：
Nonsmooth critical point theory; Discontinuous differential equation; Multivalued operator; 34A36; 47J30; 47H04;
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学科分类号：
摘要：
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.
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