By A. Bahri
(This learn be aware monitors new phenomena in selected variational difficulties of nonlinear research and geometry. the writer develops extra his rules which first seemed in a prior quantity within the sequence Pseudo-Orbits of touch shape. The linked variational challenge, that's recognized to undergo positive aspects of noncompactness is studied from a dynamical structures standpoint. Professor Bahri describes flow-lines of the gradient circulate and illustrates that the Palais-Smale could be happy alongside flow-lines whereas it fails for the variational difficulties. a brand new idea can be brought, the concept that of serious issues at infinity. He then proceeds to end up lifestyles theorems for the equations that have been thought of. this article may be of curiosity to specialist mathematicians and learn scholars in utilized and natural mathematics).