caa a22 4500 463245881 CHVBK 20180405153325.0 cr unu---uuuuu 170326e20070701xx s 000 0 eng 10.1007/s00009-007-0112-3 doi (NATIONALLICENCE)springer-10.1007/s00009-007-0112-3 Sharp Conditions for the Existence of Solutions of Second-Order Autonomous Differential Equations [Elektronische Daten] [José Cid, Rodrigo Pouso, Ricardo Enguiça] Abstract.: We prove general existence results for $$x^{\prime\prime} = f(x)g(x^{\prime}), x(0) = x_{0}, x^{\prime}(0) = x_{1},$$ where f and g need not be continuous or monotone. Moreover neither f nor g need be bounded around, respectively, x 0 and x 1, thus allowing singularities in the equation. Several other basic topics such as uniqueness, continuation, extremality and periodicity are studied in our general framework. Birkhäuser Verlag Basel/Switzerland, 2007 Second-order differential equations nationallicence discontinuous differential equations nationallicence existence nationallicence uniqueness nationallicence Cid José Departamento de Matemáticas, Universidad de Jaén, Campus Las Lagunillas, Jaén, Spain aut Pouso Rodrigo Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain aut Enguiça Ricardo Área Científica de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, 1-1950-062, Lisboa, Portugal aut Mediterranean Journal of Mathematics Birkhäuser-Verlag; www.birkhäuser.ch 4/2(2007-07-01), 191-214 1660-5446 4:2<191 2007 4 9 https://doi.org/10.1007/s00009-007-0112-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00009-007-0112-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cid José Departamento de Matemáticas, Universidad de Jaén, Campus Las Lagunillas, Jaén, Spain aut NATIONALLICENCE 700 1- Pouso Rodrigo Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain aut NATIONALLICENCE 700 1- Enguiça Ricardo Área Científica de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, 1-1950-062, Lisboa, Portugal aut NATIONALLICENCE 773 0- Mediterranean Journal of Mathematics Birkhäuser-Verlag; www.birkhäuser.ch 4/2(2007-07-01), 191-214 1660-5446 4:2<191 2007 4 9 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer