Points fixes, points critiques et problèmes aux limites. (French) Zbl 0561.34001

Mawhin, Jean

Séminaire de Mathématiques Supérieures. Séminaire Scientifique OTAN (NATO Advanced Study Institute), 92. Département de Mathématiques et de Statistique, Université de Montréal. Montréal: Les Presses de l’Université de Montréal. 162 p. $ 19.00 (1985).

These are the notes from a NATO Course in Montréal in 1983. The introduction covers the history of the qualitative theory of differential equations from Poincaré to Clarke. The first chapter refers to the method of super-solutions and sub-solutions for second order differential equations, ordinary and elliptic, with nonlinear boundary conditions. The second chapter applies the dual principle of least action to second order boundary value problems, with monotone nonlinearity. In the third chapter, the monotonicity assumption is released and the applied methods are those of super-solutions and sub-solutions, topological degree and critical points. The three appendices survey the theories of topological degree, convex functions and critical points.

Reviewer: M.Boudourides

MSC:

34-02	Research exposition (monographs, survey articles) pertaining to ordinary differential equations
34C25	Periodic solutions to ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Keywords:

method of super-solutions; sub-solutions; second order differential equations; dual principle of least action; topological degree; critical points