Results 1 to 10 of about 3,167,373 (248)
Normalized solutions for the p-Laplacian equation with a trapping potential
Advances in Nonlinear Analysis, 2023 In this article, we are concerned with normalized solutions for the pp -Laplacian equation with a trapping potential and Lr{L}^{r}-supercritical growth, where r=pr=p or 2.2.
Wang Chao, Sun Juntao
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Non-radial normalized solutions for a nonlinear Schrodinger equation [PDF]
Electronic Journal of Differential Equations, 2023 This article concerns the existence of multiple non-radial positive solutions of the L2-constrained problem $$\displaylines{-\Delta{u}-Q(\varepsilon x)|u|^{p-2}u=\lambda{u},\quad \text{in }\mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx=1,}$$ where \(Q(x)\)
Zhi-Juan Tong +2 more
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Advances in Nonlinear Analysis, 2022 This paper is devoted to investigate the existence and multiplicity of the normalized solutions for the following fractional Schrödinger equation: (P)(−Δ)su+λu=μ∣u∣p−2u+∣u∣2s∗−2u,x∈RN,u>0,∫RN∣u∣2dx=a2,\left\{\begin{array}{l}{\left(-\Delta )}^{s}u+\lambda
Li Quanqing, Zou Wenming
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Normalized solutions for Sobolev critical Schrodinger-Bopp-Podolsky systems
Electronic Journal of Differential Equations, 2023 We study the Sobolev critical Schrodinger-Bopp-Podolsky system $$\displaylines{ -\Delta u+\phi u=\lambda u+\mu|u|^{p-2}u+|u|^4u\quad \text{in }\mathbb{R}^3,\cr -\Delta\phi+\Delta^2\phi=4\pi u^2\quad \text{in } \mathbb{R}^3, }$$ under the mass constraint
Yuxin Li, Xiaojun Chang, Zhaosheng Feng
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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 , $$ \textstyle\begin{cases} -\Delta ...
Qilin Xie, Huafeng Xiao
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On Iterative Solution of the Extended Normal Equations [PDF]
SIAM Journal on Matrix Analysis and Applications, 2020 Given a full-rank matrix $A \in \mathbb{R}^{m\times n}$ ($m\geq n$), we consider a special class of linear systems $A^T\! Ax=A^T\! b+c$ with $x, c \in \mathbb{R}^{n}$ and $b \in \mathbb{R}^{m}$, which we refer to as the extended normal equations. The occurrence of $c$ gives rise to a problem with a different conditioning from the standard normal ...
Calandra, Henri +3 more
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NORMAL BGG SOLUTIONS AND POLYNOMIALS [PDF]
International Journal of Mathematics, 2012 First BGG operators are a large class of overdetermined linear differential operators intrinsically associated to a parabolic geometry on a manifold. The corresponding equations include those controlling infinitesimal automorphisms, higher symmetries and many other widely studied PDE of geometric origin.
Cap, Andreas +2 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we look for solutions to the following critical Schrödinger system $$\begin{cases} -\Delta u+(V_1+\lambda_1)u=|u|^{2^*-2}u+|u|^{p_1-2}u+\beta r_1|u|^{r_1-2}u|v|^{r_2}&{\rm in}\ \mathbb{R}^N,\\ -\Delta v+(V_2+\lambda_2)v=|v|^{2^*-2}v+|v ...
Lei Long, Xiaojing Feng
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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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