Results 11 to 20 of about 294,135 (314)

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 Schrödinger equations with potential and general nonlinearities involving critical case on large convex domains

Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we study the following Schrödinger equations with potentials and general nonlinearities \begin{equation*} \begin{cases} -\Delta u+V(x)u+\lambda u=|u|^{q-2}u+\beta f(u), \\ \int |u|^2dx=\Theta, \end{cases} \end{equation*} both on ...
Jun Wang, Zhaoyang Yin
doaj   +2 more sources

Existence and non-degeneracy of the normalized spike solutions to the fractional Schrödinger equations

Advances in Nonlinear Analysis
The present study investigates the existence and non-degeneracy of normalized solutions for the following fractional Schrödinger equation: (−Δ)su+V(x)u=aup+μu,x∈RN,u∈Hs(RN){\left(-\Delta )}^{s}u+V\left(x)u=a{u}^{p}+\mu u,\hspace{1.0em}x\in {{\mathbb{R}}}^
Guo Qing, Zhang Yuhang
doaj   +2 more sources

Positive Normalized Solutions to a Kind of Fractional Kirchhoff Equation with Critical Growth [PDF]

Fractal and Fractional
In this paper, we have investigated the existence of normalized solutions for a class of fractional Kirchhoff equations involving nonlinearity and critical nonlinearity. The nonlinearity satisfies L2-supercritical conditions.
Shiyong Zhang, Qiongfen Zhang
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

Existence of normalized solutions for the Schrödinger equation

Communications in Analysis and Mechanics, 2023
In this paper, we devote to studying the existence of normalized solutions for the following Schrödinger equation with Sobolev critical nonlinearities. $ \begin{align*} &\left\{\begin{array}{ll} -\Delta u = \lambda u+\mu\lvert u \rvert^{q-2}u+\
Shengbing Deng, Qiaoran Wu
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

On Iterative Solution of the Extended Normal Equations [PDF]

SIAM Journal on Matrix Analysis and Applications, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Henri Calandra, Serge Gratton, Elisa Riccietti, Xavier Vasseur   +3 more
openaire   +4 more sources