What question did this study set out to answer?

The study aims to extend existing results for vector Dirichlet problems involving implicit differential equations and inclusions.

March 27, 2026Open Access

Multiple Solutions of Vector Dirichlet Problems to Implicit Differential Equations and Inclusions in Billiard Spaces

Key Points

The study aims to extend existing results for vector Dirichlet problems involving implicit differential equations and inclusions.
Consider explicit differential inclusions with upper-Carathéodory right-hand sides.
Examine implicit differential inclusions with Marchaud right-hand sides.
Generalize earlier results to multivalued or discontinuous settings.
Extend multiplicity results for implicit boundary value problems.
Demonstrated the existence of multiple solutions for vector Dirichlet problems.
Extended results for complex boundary value problems in a rare multivalued context.

Abstract

Abstract The problem from the title will be considered separately for explicit differential inclusions with upper-Carathéodory right-hand sides and implicit differential inclusions with Marchaud right-hand sides. In the first case, several earlier results for differential equations will be generalized to a multivalued or discontinuous setting. In the second case, which is a main object of our study, quite rare multiplicity results for implicit boundary value problems will be extended.

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