The Leray-Schauder method vs translation along the trajectories: Which is better in the theory of boundary value problems?

DOI10.1023/A:1012467401915zbMath1012.47045OpenAlexW54899562MaRDI QIDQ1603136

V. V. Filippov

Publication date: 6 August 2002

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1012467401915

zbMATH Keywords

Cauchy problemexistence of periodic solutionsLeray-Schauder theorymethod of translation along the trajectoriesprinciple of parameter continuation

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Nonlinear boundary value problems for ordinary differential equations (34B15) Periodic solutions to ordinary differential equations (34C25) Degree theory for nonlinear operators (47H11) Applications of operator theory to differential and integral equations (47N20)

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Partial mappings, Čech homology and ordinary differential equations ⋮ On periodic solutions of ordinary differential equations with discontinuous right-hand side ⋮ The Carathéodory and Plis-Davy theorems, Krasovsky regularization, and continuous dependence of solutions on parameters on the right-hand side

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