Teoria di Lusternik-Schnirelman su varietà con bordo negli spazi di Hilbert
The compact category and mulitple periodic solutions of Hamiltionian systems on symmetric starshaped energy surfaces.
The computation of the index of a Morse function at a critical point.
The Conley index in Hilbert spaces and its applications
We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals having...
The CR Yamabe conjecture the case
Let be a compact CR manifold of dimension with a contact form , and its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form on conformal to which has a constant Webster curvature. This problem is equivalent to the existence of a function such that , on . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where and is not locally CR equivalent to the sphere of . In a join work with R. Yacoub, the CR Yamabe problem...
The Critical Points Theory for the Closed Geodesics Problem.
The Dirichlet-problem for harmonic maps from the disk into a lorentzian warped product
The dual variational principle and discontinuous elliptic problems with strong resonance at infinity.
The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations.
The existence of critical values in an abstract perturbation problem.
The existence of polar non-degenerate functions on a topological manifold
The existence of positive solution to some asymptotically linear elliptic equations in exterior domains.
In this paper, we are concerned with the asymptotically linear elliptic problem -Δu + λ0u = f(u), u ∈ H01(Ω) in an exterior domain Ω = RnO (N ≥ 3) with O a smooth bounded and star-shaped open set, and limt→+∞ f(t)/t = l, 0 < l < +∞. Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.
The generalized Conley index and multiple solutions of semilinear elliptic problems.
The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions
In a previous note the author gave a generalisation of Witten’s proof of the Morse inequalities to the model of a complex singular curve and a stratified Morse function . In this note a geometric interpretation of the complex of eigenforms of the Witten Laplacian corresponding to small eigenvalues is provided in terms of an appropriate subcomplex of the complex of unstable cells of critical points of .
The index of the second variation of a control system
The Lagrange Intersections for (CPn, RPn).
The minimal period problem of classical hamiltonian systems with even potentials
The number of critical points in Morse approximations
The structure of the critical set in the general mountain pass principle
The use of Cerami sequences in critical point theory.