117 research outputs found
Existence of ground states for a modified nonlinear Schrodinger equation
In this paper we prove existence of ground state solutions of the modified
nonlinear Schrodinger equation: under some hypotheses on .
This model has been proposed in the theory of superfluid films in plasma
physics. As a main novelty with respect to some previous results, we are able
to deal with exponents . The proof is accomplished by minimization
under a convenient constraint
A minimization problem for the Nonlinear Schr¨odinger-Poisson type Equation
In this paper we consider the stationary solutions of the Schr¨odinger-Poisson equation:it + − (|x|−1 | |2) + | |p−2 = 0 in R3. We are interested in the existence of standing waves, that is solutions of type (x, t) = u(x)e−i!t, where ! 2 R, with fixed L2 −norm. Then we are reduced to a constrained minimization problem. The main difficulty is the compactness of the minimizing sequences since the related functional is invariant y translations. By using some abstract results, we give a positive answer, showing that the minimum of the functional is achieved on small L2 −spheres in the case 2 < p < 3 and large L2 − spheres in the case 3 < p < 10/3. The results exposed here can be found with more details in [6] and [7]. Â
Klein-Gordon-Maxwell System in a bounded domain
This paper is concerned with the Klein-Gordon-Maxwell system in a bounded
spatial domain. We discuss the existence of standing waves
in equilibrium with a purely electrostatic field
. We assume an homogeneous Dirichlet boundary
condition on and an inhomogeneous Neumann boundary condition on . In
the "linear" case we characterize the existence of nontrivial solutions for
small boundary data. With a suitable nonlinear perturbation in the matter
equation, we get the existence of infinitely many solutions.Comment: 17 page
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