On the Morse Number of Embedded and Non-Embedded Minimal Immersions Spanning Wires on the Boundary of Special Bodies in IR3.
On the Moser-Onofri and Prékopa-Leindler inequalities.
Using elementary convexity arguments involving the Legendre transformation and the Prékopa-Leindler inequality, we prove the sharp Moser-Onofri inequality, which says that1/16π ∫|∇φ|2 + 1/4π ∫ φ - log (1/4π ∫ eφ) ≥ 0for any funcion φ ∈ C∞(S2).
On the mountain pass lemma
On the multiplicity of critical points for parameterized functionals on reflexive Banach spaces
Some general multiplicity results for critical points of parameterized functionals on reflexive Banach spaces are established. In particular, one of them improves some aspects of a recent result by B. Ricceri. Applications to boundary value problems are also given.
On the multiplicity of eigenvalues of conformally covariant operators
Let be a compact Riemannian manifold and an elliptic, formally self-adjoint, conformally covariant operator of order acting on smooth sections of a bundle over . We prove that if has no rigid eigenspaces (see Definition 2.2), the set of functions for which has only simple non-zero eigenvalues is a residual set in . As a consequence we prove that if has no rigid eigenspaces for a dense set of metrics, then all non-zero eigenvalues are simple for a residual set of metrics in the -topology....
On the multiplicity of solutions for a fully nonlinear Emden-Fowler equation.
On the natural operators of Bianchi type
On the natural operators transforming vector fields to the -th tensor power
On the natural transformations of Weil bundles
First we deduce some general results on the covariant form of the natural transformations of Weil functors. Then we discuss several geometric properties of these transformations, special attention being paid to vector bundles and principal bundles.
On the necessity of gaps
Recent papers have studied the existence of phase transition solutions for Allen–Cahn type equations. These solutions are either single or multi-transition spatial heteroclinics or homoclinics between simpler equilibrium states. A sufficient condition for the construction of the multitransition solutions is that there are gaps in the ordered set of single transition solutions. In this paper we explore the necessity of these gap conditions.
On the Neumann Problem for the Nonlinear Parabolic Equation of Eells-Sampson and Harmonie Mappings.
On the nonlinear elastic simply supported beam equation.
On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity
We consider the Neumann problem for the equation , u ∈ H¹(Ω), where Q is a positive and continuous coefficient on Ω̅ and λ is a parameter between two consecutive eigenvalues and . Applying a min-max principle based on topological linking we prove the existence of a solution.
On the notion of -completeness of a stochastic flow on a manifold.
On the notion of potential for mappings between linear spaces. A generalized version of the Poincaré lemma
An approach to the theory of linear differential forms in a radial subset of an (arbitrary) real linear space without a Banach structure is proposed. Only intrinsic (partially linear) topologies on are (implicitly) involved in the definitions and statements. Then a mapping , with , real linear spaces and a radial subset of , is considered. After showing a representation theorem of those bilinear forms on for which
On the Novikov complex for rational Morse forms
On the Number of Closed Geodesics on Projective Spaces.
On the number of minimal two-spheres of small area in manifolds with curvature bounded above.
On the number of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds.
On the Numerical Analysis of the Von Karman Equations : Mixed Finite Element Approximation and Continuation Techniques.