M. Degiovanni
Some basic tools of critical point theory
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MSC:
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58E05 Abstract critical point theory (Morse theory,
Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
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35J65 Nonlinear boundary value problems for linear elliptic PDE;
boundary value problems for nonlinear elliptic PDE
Abstract:
The basic tools of abstract critical point theory, namely
pseudo-gradient vector fields, deformation theorems,
linking theorems, are presented.
The continuity, differentiability and compactness of the
Nemytskij operator between Lebesgue spaces and Sobolev spaces
is also studied.
Keywords:
critical point theory, deformation theorems, linking theorems,
Nemytskij operator