Band 3, Heft 1

We look for solutions of a nonlinear perturbed Schrödinger equation with nonhomogeneous Dirichlet boundary conditions. By using a perturbation method introduced by Bolle, we prove the existence of multiple solutions in spite of the lack of the symmetry of the problem.

We study the properties of the following equations with absorption or source term -Δ p u = ± |u| q-1 u + μ, in a domain Ω of ℝ N , where 1 < p < N, q > p-1, and μ is a Radon measure on Ω. We introduce a notion of local entropy solution, and give necessary conditions on μ for the existence of solutions, in terms of capacity. The question of removability of sets is also considered, as well as some stability results. Finally we give existence results in ℝ N for the case of absorption.

In this paper, we describe new results in Contact Form Geometry and Yamabe-type problems. We provide in Contact Form Geometry a new way to use the results of [10] and define a homology. We emphasize the connections with the area of pseudeholomorphic curves. We relate, in Yamabe-type problems, smooth and singular solutions to this kind of equations. These new results indicate that noncompact phenomena should be understood in terms of Configuration Spaces in both directions and more generally in the wider area of Conformal Geometry.

In this paper we prove the existence of infinitely many solitary waves with non vanishing angular momentum for Nonlinear Schrödinger Equation: where ψ, : ℝ 3 × ℝ → ℂ and 2 < p < 6.