126 research outputs found
Multiple positive solutions for a Schr\"odinger-Poisson-Slater system
In this paper we investigate the existence of positive solutions to the
following Schr\"odinger-Poisson-Slater system [c]{ll} - \Delta u+ u +
\lambda\phi u=|u|^{p-2}u & \text{in} \Omega -\Delta\phi= u^{2} & \text{in}
\Omega u=\phi=0 & \text{on} \partial\Omega. where is a bounded domain
in is a fixed positive parameter and
. We prove that if is "near" the critical Sobolev
exponent , then the number of positive solutions is greater then the
Ljusternik-Schnirelmann category of .Comment: added references and improved the resul
Nonlinear Schr\"odinger equation in the Bopp-Podolsky electrodynamics: solutions in the electrostatic case
We study the following nonlinear Schr\"odinger-Bopp-Podolsky system with
. We prove existence and nonexistence results depending on the
parameters . Moreover we also show that, in the radial case, the solutions
we find tend to solutions of the classical Schr\"odinger-Poisson system as
.Comment: 30 pages, the nonexistence result has been improve
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 Schršodinger-Poisson type Equation
In this paper we consider the stationary solutions of the Schršodinger-Poisson equation:it + â (|x|â1 | |2) + | |pâ2 = 0 in R3. We are interested in the existence of standing waves, that is solutions of type (x, t) = u(x)eâi!t, where ! 2 R, with fixed L2 ânorm. 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 âspheres in the case 2 < p < 3 and large L2 â spheres in the case 3 < p < 10/3. The results exposed here can be found with more details in [6] and [7]. Â
On a generalized Kirchhoff equation with sublinear nonlinearities
In this paper we consider a generalized Kirchhoff? equation in a bounded
domain under the effect of a sublinear nonlinearity. Under suitable assumptions
on the data of the problem we show that, with a simple change of variable, the
equation can be reduced to a classical semilinear equation and then studied
with standard tools.Comment: 13 page
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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