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Existence principles for differential equations and systems of equations

  • John W. Lee
  • Donal O’Regan
Chapter
Part of the NATO ASI Series book series (ASIC, volume 472)

Abstract

These lectures cover basic existence and sometimes uniqueness principles for systems of ordinary differential equations and for equations in Banach spaces. The existence principles are established by means of topological methods based on nonlinear alternatives for compact maps and for contractive maps. The initial analysis treats both classical and Carathéodory problems on compact intervals simultaneously and in a classical setting by recasting the boundary value problem as an equivalent integro-differential equation. Later problems with more general singularities and/or unbounded intervals are treated.

Keywords

Banach Space Nonlinear Boundary Condition Fixed Point Problem Lebesgue Dominate Convergence Theorem Nonlinear Alternative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • John W. Lee
    • 1
  • Donal O’Regan
    • 2
  1. 1.Department of MathematicsOregon State UniversityCorvallisUSA
  2. 2.Department of MathematicsUniversity College GalwayGalwayIreland

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