Invariant sets of descending flow in critical point theory with applications to nonlinear differential equations

Properties of invariant sets uf descending flow defined by a pseudogradient vector field of a functional in a Banach space are studied. In this way, s everal critical points can be found by constructing different invariant set s on which the functional is bounded below. Under suitable conditions. the existence of at least four critical points of a functional is proved, each critical point bring in a certain invariant set. The theoretical results ar e applied to nonlinear elliptic boundary value problems and nonlinear syste ms of ordinary differential equations. In variant eases. at least four solu tions are obtained for these equations. (C) 2001 Academic Press.