Results 51 to 60 of about 1,711 (146)

About existence and regularity of positive solutions for a quasilinear Schrödinger equation with singular nonlinearity

Electronic Journal of Qualitative Theory of Differential Equations, 2020
We establish the existence of positive solutions for the singular quasilinear Schrödinger equation \begin{equation*} \begin{cases} -\Delta u -\Delta (u^{2})u=h(x) u^{-\gamma} + f(x,u)& \mbox{in } \Omega,\\ u(x)=0&\mbox{on }\partial \Omega, \end{cases ...
Ricardo Alves, Mariana Reis
doaj   +1 more source

Existence of infinitely many radial and non-radial solutions for quasilinear Schrödinger equations with general nonlinearity

Electronic Journal of Qualitative Theory of Differential Equations, 2017
In this paper, we prove the existence of many solutions for the following quasilinear Schrödinger equation \begin{equation*} -\Delta u - u\Delta(|u|^2) + V(|x|)u = f(|x|,u),\qquad x \in \mathbb{R}^N. \end{equation*} Under some generalized assumptions on $
Jianhua Chen, Xianhua Tang, Jian Zhang, Huxiao Luo   +3 more
doaj   +1 more source

Finite‐Dimensional Reductions and Finite‐Gap‐Type Solutions of Multicomponent Integrable PDEs

Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.
ABSTRACT The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well‐known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup ...
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev   +2 more
wiley   +1 more source

Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations [PDF]

, 2015
Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the recent ...
Paleari, S., Pelinovsky, D., Penati, T.
core   +2 more sources

On the wave turbulence theory of 2D gravity waves, I: Deterministic energy estimates

Communications on Pure and Applied Mathematics, Volume 78, Issue 2, Page 211-322, February 2025.
Abstract Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV‐type equations. However, our situation
Yu Deng, Alexandru D. Ionescu, Fabio Pusateri   +2 more
wiley   +1 more source

Antisymmetric solutions for a class of quasilinear defocusing Schrödinger equations

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this paper we consider the existence of antisymmetric solutions for the quasilinear defocusing Schrödinger equation in $H^1(\mathbb{R}^N)$: $$ -\Delta u +\frac{k}{2}u \Delta u^2+V(x)u=g(u), $$ where $N\geq 3$, $V(x)$ is a positive continuous potential,
Janete Soares Gamboa, Jiazheng Zhou
doaj   +1 more source

Infinitely many periodic solutions for a class of fractional Kirchhoff problems

, 2019
We prove the existence of infinitely many nontrivial weak periodic solutions for a class of fractional Kirchhoff problems driven by a relativistic Schr\"odinger operator with periodic boundary conditions and involving different types of ...
Ambrosio, Vincenzo
core   +1 more source

Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains [PDF]

, 2012
We consider a semilinear elliptic problem with a nonlinear term which is the product of a power and the Riesz potential of a power. This family of equations includes the Choquard or nonlinear Schroedinger--Newton equation. We show that for some values of
Agmon, Agmon, Ambrosetti, Bidaut-Véron, Brezis, Brezis, Caristi, Choquard, Cycon, Fall, Frank, Gidas, Gilbarg, Herbst, Jean Van Schaftingen, Kato, Kondratiev, Lenzmann, Lieb, Lieb, Lieb, Lions, Lions, Liskevich, Ma, Menzala, Menzala, Mitidieri, Moroz, Moroz, Moroz, Pekar, Penrose, Pinchover, Quittner, Riesz, Secchi, Stein, Tod, Vitaly Moroz, Wei   +40 more
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Algebraic Lower Bounds on the Spatial Analyticity Radius for Higher Order Nonlinear Schrödinger Equations

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
We investigate the initial value problem associated to the higher order nonlinear Schrödinger equation i∂tu+−1j+1∂x2ju=u2ju x,t≠0∈ℝ,ux,0=u0x, where j ≥ 2 is any integer, u is a complex valued function, and the initial data u0 is real analytic on ℝ and has a uniform radius of spatial analyticity σ0 in the space variable.
Tegegne Getachew, Birilew Belayneh, Betre Shiferaw, Huaiqin Wu   +3 more
wiley   +1 more source

The Calogero–Moser derivative nonlinear Schrödinger equation

Communications on Pure and Applied Mathematics, Volume 77, Issue 10, Page 4008-4062, October 2024.
Abstract We study the Calogero–Moser derivative nonlinear Schrödinger NLS equation i∂tu+∂xxu+(D+|D|)(|u|2)u=0$$\begin{equation*} i\partial _t u +\partial _{xx} u + (D+|D|)(|u|^2) u =0 \end{equation*}$$posed on the Hardy–Sobolev space H+s(R)$H^s_+(\mathbb {R})$ with suitable s>0$s>0$.
Patrick Gérard, Enno Lenzmann
wiley   +1 more source