406 research outputs found
On a fourth order nonlinear Helmholtz equation
In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz
equation in for positive, bounded and -periodic functions . Using
the dual method of Evequoz and Weth, we find solutions to this equation and
establish some of their qualitative properties
One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in R
In this paper, we prove an analogue of Gibbons' conjecture for the extended
fourth order Allen-Cahn equation in R N , as well as Liouville type results for
some solutions converging to the same value at infinity in a given direction.
We also prove a priori bounds and further one-dimensional symmetry and rigidity
results for semilinear fourth order elliptic equations with more general
nonlinearities
Existence of positive solutions of a superlinear boundary value problem with indefinite weight
We deal with the existence of positive solutions for a two-point boundary
value problem associated with the nonlinear second order equation
. The weight is allowed to change its sign. We assume
that the function is
continuous, and satisfies suitable growth conditions, so as the case
, with , is covered. In particular we suppose that is
large near infinity, but we do not require that is non-negative in a
neighborhood of zero. Using a topological approach based on the Leray-Schauder
degree we obtain a result of existence of at least a positive solution that
improves previous existence theorems.Comment: 12 pages, 4 PNG figure
Stationary solutions of the nonlinear Schr\"odinger equation with fast-decay potentials concentrating around local maxima
We study positive bound states for the equation where is a real
parameter, and is a nonnegative
potential. Using purely variational techniques, we find solutions which
concentrate at local maxima of the potential without any restriction on the
potential.Comment: 25 pages, reformatted the abstract for MathJa
Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence
We prove existence and multiplicity results for finite energy solutions to
the nonlinear elliptic equation where is a radial domain (bounded or
unbounded) and satisfies on if and as
if is unbounded. The potential may be vanishing or unbounded at
zero or at infinity and the nonlinearity may be superlinear or sublinear.
If is sublinear, the case with is also considered.Comment: 29 pages, 8 figure
First escaping fast ion mesurements in ITER-like geometry using an activation probe
More research is needed to develop suitable diagnostics for measuring alpha particle confinement in ITER and techniques relevant for fusion reactor conditions need further development. Based on nuclear reactions, the activation probe is a novel concept first tested in JET. It may offer a more robust solution for performing alpha particle measurements in ITER. This paper describes the first escaping fast ion measurements performed at ASDEX Upgrade (AUG) tokamak using an activation probe. A detailed analysis, outside the scope of this contribution, will be published in a journal paper.JRC.D.4-Standards for Nuclear Safety, Security and Safeguard
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