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Asymptotics of the Solutions of the Random Schrödinger Equation
Asymptotics of the Solutions Random Schrö dinger Equation
2015/7/14
We consider solutions of the Schrödinger equation with a weak time-dependent random potential. It is shown that when the two-point correlation function of the potential is rapidly decaying, then ...
MULTIPLE MIXED STATES OF NODAL SOLUTIONS FOR NONLINEAR SCHR ODINGER SYSTEMS
MULTIPLE MIXED STATES NONLINEAR SCHR ODINGER SYSTEMS
2014/9/26
In this paper we develop a general critical point theory to deal with existence
and locations of multiple critical points produced by minimax methods in relation to mul-tiple invariant sets of the as...
Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation
the first Painlevé hierarchy non-generic critical behavior the KdV equation
2011/8/23
Abstract: We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the d...
A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold
Asymptotically hyperbolic manifold Constraint equations Conformal method
2011/3/2
We construct solutions of the constraint equation with non constant mean curvature on an
asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain expo...
Existence and approximation of probability measure solutions to models of collective behaviors
Existence approximation of probability measure models of collective behaviors
2011/1/20
In this paper we consider first order differential models of collective behaviors of groups
of agents based on the mass conservation equation. Models are formulated taking the spatial
distribution o...
Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory
singular perturbation nondegenerate critical points Morse theory
2011/2/28
Given (M, g0) we consider the problem −"2g0+hu + u = (u+)p−1 with (", h) ∈ (0, ¯") × B. Here B is a ball centered at 0 with radius in the Banach space of all Ck symmetric covaria...
Eigenfunctions and Very Singular Similarity Solutions of Odd-Order Nonlinear Dispersion PDEs
Eigenfunctions Very Singular Similarity Solutions Odd-Order Nonlinear Dispersion PDEs
2010/11/11
Asymptotic properties of solutions of odd-order nonlinear dispersion equations are studied. The global in time similarity solutions, which lead to eigenfunctions of the rescaled ODEs, are constructed....
Jacob's ladders, Bessel's functions and the asymptotic solutions of a new class of nonlinear integral equations
Jacob's ladders Bessel's functions the asymptotic solutions
2010/11/19
It is shown in this paper that there is a connection between the Riemann zeta-function $\zf$ and the Bessel's functions. In this direction, a new class of the nonlinear integral equations is introduce...
Solutions of the Cheeger problem via torsion functions
the Cheeger problem torsion functions
2010/11/19
The Cheeger problem for a bounded domain $\Omega\subset\mathbb{R}^{N}$, $N>1$ consists in minimizing the quotients $|\partial E|/|E|$ among all smooth subdomains $E\subset\Omega$ and the Cheeger cons...
Amusing properties of Klein-Gordon solutions on manifolds with variable geometry
properties Klein-Gordon solutions on manifolds variable geometry
2010/12/16
This work develops the recent proposition to use dimensional reduction from the four-imensional space-time to the one with a smaller number of dimensions (1 + d); d < 3 at high enough energy.To this g...
Asymptotic stability of solutions to abstract differential equations
Nonlinear inequality Asymptotic stability Abstract differential equations
2010/12/15
An evolution problem for abstract differential equations is studied. The typical problem is:
˙ u = A(t)u+F(t,u), t ≥ 0; u(0) = u0; ˙ u =du dt ∗)Here A(t) is a linear bounded operator in a Hilbe...
Positive solutions for Second-Order Boundary Value Problem with Integral Boundary Conditions at Resonance on a Half-Line
Boundary value problem Resonance Cone Positive solution Coincidence
2010/1/22
This paper deals with the second order boundary value problem with integral boundary conditions on a half-line: a.e. in A new result on the existence of positive solutions is obta...
Existence of Regular Solutions for a One-Dimensional Simplified Perfect-Plastic Problem with a Unilateral Gradient Constraint
Regular Solutions Unilateral Gradient Constraint One-Dimensional Simplified Perfect-Plastic Problem
2009/2/5
This work is devoted to the study of the existence of "regular" solutions for a one-dimensional problem with unilateral constrained gradient in Perfect-Plasticity.
The particularity of this problem ...
Nonexistence of Solutions in Nonconvex Multidimensional Variational Problems
Gradient Young measures extreme points Cantor sets integration factors Bauer principle nonattainment
2009/1/19
In the scalar n-dimensional situation, the extreme points in the set of certain gradient Lp-Young measures
are studied. For n = 1, such Young measures must be composed from Diracs, while for n µ...
Summability of the Solutions to Nonlinear Parabolic Equations with Measure Data
summability nonlinear parabolic equations measure data
2009/1/13
In this paper, we give an improvement of the summability of solutions to nonlinear parabolic equations with measure data.