Results 11 to 20 of about 299,484 (312)

Normalized solutions to nonautonomous Kirchhoff equation

Communications in Analysis and Mechanics
In this paper, we studied the existence of normalized solutions to the following Kirchhoff equation with a perturbation:$ \left\{ \begin{aligned} &-\left(a+b\int _{\mathbb{R}^{N}}\left | \nabla u \right|^{2} dx\right)\Delta u+\lambda u = |u|^{p-2}
Xin Qiu, Zeng Qi Ou, Ying Lv
doaj   +4 more sources

Normalized solutions for nonlinear Kirchhoff type equations in high dimensions

Electronic Research Archive, 2022
We study the normalized solutions for nonlinear Kirchhoff equation with Sobolev critical exponent in high dimensions $ \mathbb{R}^N(N\geqslant4) $. In particular, in dimension $ N = 4 $, there is a special phenomenon for Kirchhoff equation that the mass ...
Lingzheng Kong, Haibo Chen
doaj   +2 more sources

Normalized solutions of NLS equations with mixed nonlocal nonlinearities

Advances in Nonlinear Analysis
We study the existence and nonexistence of normalized solutions for the nonlinear Schrödinger equation with mixed nonlocal nonlinearities: −Δu=λu+μ(Iα∗∣u∣p)∣u∣p−2u+(Iα∗∣u∣q)∣u∣q−2uinRN,∫RN∣u∣2dx=c,\left\{\begin{array}{ll}-\Delta u=\lambda u+\mu \left({I ...
Zhang Zhenyu, Sun Juntao
doaj   +2 more sources

Multiplicity and concentration of normalized solutions for a Kirchhoff type problem with $ L^2 $-subcritical nonlinearities

Communications in Analysis and Mechanics
In this paper, we studied the existence of multiple normalized solutions to the following Kirchhoff type equation:$ \begin{equation*} \begin{cases} -\left(a\varepsilon^2+b\varepsilon\int_{\mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+V(x)u = \mu u+f(u) &
Yangyu Ni, Jijiang Sun, Jianhua Chen
doaj   +2 more sources

Normalized solutions for Kirchhoff-Carrier type equation

AIMS Mathematics, 2023
In this paper, we study the following Kirchhoff-Carrier type equation $ -\left(a+bM\left(|\nabla u|_{2}, |u|_{\tau}\right)\right)\Delta u-\lambda u = |u|^{p-2}u, \quad \ {\rm in}\ \mathbb{R}^{3}, $ where $ a, \ b > 0 $ are constants ...
Jie Yang, Haibo Chen
doaj   +1 more source

Normalized solutions for the discrete Schrödinger equations

Boundary Value Problems, 2023
In the present paper, we consider the existence of solutions with a prescribed l 2 $l^{2}$ -norm for the following discrete Schrödinger equations, { − Δ 2 u k − 1 − f ( u k ) = λ u k k ∈ Z , ∑ k ∈ Z | u k | 2 = α 2 , $$ \textstyle\begin{cases} -\Delta ...
Qilin Xie, Huafeng Xiao
doaj   +1 more source

Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians

Advanced Nonlinear Studies, 2022
The purpose of this article is to establish sharp conditions for the existence of normalized solutions to a class of scalar field equations involving mixed fractional Laplacians with different orders.
Luo Tingjian, Hajaiej Hichem
doaj   +1 more source

NORMAL BGG SOLUTIONS AND POLYNOMIALS [PDF]

International Journal of Mathematics, 2012
First BGG operators are a large class of overdetermined linear differential operators intrinsically associated to a parabolic geometry on a manifold. The corresponding equations include those controlling infinitesimal automorphisms, higher symmetries and many other widely studied PDE of geometric origin.
Cap, Andreas, Gover, Rod, Hammerl, Matthias   +2 more
openaire   +5 more sources

Normalized solutions for a critical fractional Choquard equation with a nonlocal perturbation

Advances in Nonlinear Analysis, 2023
In this article, we study the fractional critical Choquard equation with a nonlocal perturbation: (−Δ)su=λu+α(Iμ*∣u∣q)∣u∣q−2u+(Iμ*∣u∣2μ,s*)∣u∣2μ,s*−2u,inRN,{\left(-{\Delta })}^{s}u=\lambda u+\alpha \left({I}_{{\mu }^{* }}\hspace{-0.25em}{| u| }^{q}){| u|
Lan Jiali, He Xiaoming, Meng Yuxi
doaj   +1 more source

Normalized solutions for nonlinear Schrödinger systems [PDF]

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2017
We consider the existence of normalized solutions in H1(ℝN) × H1(ℝN) for systems of nonlinear Schr¨odinger equations, which appear in models for binary mixtures of ultracold quantum gases. Making a solitary wave ansatz, one is led to coupled systems of elliptic equations of the formand we are looking for solutions satisfyingwhere a1> 0 and a2> 0 ...
Bartsch, Thomas, Jeanjean, Louis
openaire   +3 more sources