Measure Differential Equations with a General Nonlocal Condition
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The paper is concerned with the existence of regulated solutions for measure differential equations with a nonlocal condition involving a set-valued map. The first result, imposing Kurzweil-Stieltjes integrability together with a powerful convergence result, is available in finite dimensional spaces. The second one, assuming Lebesgue-Stieltjes integrability together with conditions expressed in terms of Hausdorff measure of non-compactness, works in general Banach spaces.
- University of Chile Chile
Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.), measure differential equations, Lebesgue-Stieltjes integral, nonlocal conditions, Denjoy and Perron integrals, other special integrals, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Nonlocal and multipoint boundary value problems for ordinary differential equations, regulated functions, Kurzweil-Stieltjes integral, Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.), measure differential equations, Lebesgue-Stieltjes integral, nonlocal conditions, Denjoy and Perron integrals, other special integrals, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Nonlocal and multipoint boundary value problems for ordinary differential equations, regulated functions, Kurzweil-Stieltjes integral, Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
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