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Normalized solutions to nonautonomous Kirchhoff equation
Communications in Analysis and MechanicsIn 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
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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
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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
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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 ...
Thomas Bartsch, Louis Jeanjean
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Normalized solutions for the Klein Gordon-Dirac system
Rendiconti Lincei, Matematica e Applicazioni, 2022 We prove the existence of a stationary solution for the system describing the interaction between an electron coupled with a massless scalar field (a photon). We find a solution, with fixed L^2 -norm, by variational methods, as a critical point of an energy functional.
Vittorio Coti Zelati, Margherita Nolasco
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Normalized solutions for pseudo-relativistic Schrödinger equations
Communications in Analysis and MechanicsIn this paper, we consider the existence and multiplicity of normalized solutions to the following pseudo-relativistic Schrödinger equations $ \begin{equation*} \left\{ \begin{array}{lll} \sqrt{-\Delta+m^2}u +\lambda u = \vartheta |u|^{p-2}v +|u|^{2 ...
Xueqi Sun, Yongqiang Fu, Sihua Liang
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Normalized solutions of Schrödinger equations involving Moser-Trudinger critical growth
Advances in Nonlinear AnalysisIn this article, we are concerned with the nonlinear Schrödinger equation −Δu+λu=μ∣u∣p−2u+f(u),inR2,-\Delta u+\lambda u=\mu {| u| }^{p-2}u+f\left(u),\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{2}, having prescribed ...
Li Gui-Dong, Zhang Jianjun
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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
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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.
A. R. Gover +3 more
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