A Morse Theory for Massive Particles and Photons in General Relativity

In this paper we develop a Morse Theory for timelike geodesics parameterized by a constant multiple of proper time. The results are obtained using an extension to the timelike case of the relativistic Fermat Principle, and techniques from Global Analysis on infinite dimensional manifolds. In the second part of the paper we discuss a limit process that allows to obtain also a Morse theory for light rays

Existence and multiplicity results for resonant fractional boundary value problems

We study a Dirichlet-type boundary value problem for a pseudo-differential equation driven by the fractional Laplacian, with a non-linear reaction term which is resonant at infinity between two non-principal eigenvalues: for such equation we prove existence of a non-trivial solution. Under further assumptions on the behavior of the reaction at zero, we detect at least three non-trivial solutions (one positive, one negative, and one of undetermined sign). All results are based on the properties of weighted fractional eigenvalues, and on Morse theory

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.Comment: 39 pages, LaTeX2e, amsar

Existence of multiple nontrivial solutions for semilinear elliptic problems

AbstractThe aim of this paper is to prove the existence of multiple nontrivial solutions to a semilinear elliptic problem at resonance. The proofs used here are based on combining the Morse theory and the minimax methods

Three nontrivial solutions for the p-Laplacian Neumann problems with a concave nonlinearity near the origin

We consider a nonlinear Neumann problem driven by the p- Laplacian, with a right-hand side nonlinearity which is concave near the origin. Using variational techniques, combined with the method of upper-lower solutions and with Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have a constant sign (one positive and one negative).FCTPOCI/MAT/55524/200

Multiple Solutions for Resonant Elliptic Equations via Local Linking Theory and Morse Theory

AbstractWe consider two classes of elliptic resonant problems. First, by local linking theory, we study the double-double resonant case and obtain three solutions. Second, we introduce some new conditions and compute the critical groups both at zero and at infinity precisely. Combining Morse theory, we get three solutions for the completely resonant case