Critical Points at Infinity in Some Variational Problems (Pitman Research Notes in Mathematics Series,) by Abbas Bahri (PDF)

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(This research Note displays new phenomena in chosen variational problems of nonlinear analysis and geometry. The author develops further his ideas which first appeared in a previous volume in the series Pseudo-Orbits of Contact Form. The associated variational problem, which is known to bear features of noncompactness is studied from a dynamical systems point of view. Professor Bahri describes flow-lines of the gradient flow and illustrates that the Palais-Smale condition can be satisfied along flow-lines while it fails for the variational problems. A new concept is also introduced, the concept of critical points at infinity. He then proceeds to prove existence theorems for the equations which have been considered. This text should be of interest to professional mathematicians and research students in applied and pure mathematics).

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⭐in t his book foundational ideas and new variational technics are invented. It is always amazing to see how the author into all the details of involved computations !

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