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1. Introduction We aim at finding a simple, easily applicable in practice, way to determine whether an explicitly given pointwise-constrained control BVP (boundary value problem), using two controls in the plane R 2 , does possess bang-bang solutions. The famous Lyapunov theorem on the convexity of the range of vector measures is not valid here, without extra hypotheses, since bang-bang solutions do not always exist, due to our pointwise state-constraint.
This is an early access version, the complete PDF, HTML, and XML versions will be available soon. Open AccessArticle by Clara Carlota *,† and António Ornelas † Departamento de Matemática, CIMA, Universidade de Évora, 7000-671 Évora, Portugal * Author to whom correspondence should be addressed. † These authors contributed equally to this work.
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