Results 11 to 20 of about 1,045,959 (290)
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 , $$ \textstyle\begin{cases} -\Delta ...
Qilin Xie, Huafeng Xiao
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we look for solutions to the following critical Schrödinger system $$\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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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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Normalized solutions of Kirchhoff equations with Hartree-type nonlinearity
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In the present paper, we prove the existence of the solutions (λ, u) ∈ ℝ × H1(ℝ3) to the following Kirchhoff equations with the Hartree-type nonlinearity under the general mass supercritical settings, {-(a+b∫ℝ3|∇u|2dx)Δu-λu=[Iα*(K(x)F(u))]K(x)f(u),u∈H1 ...
Yuan Shuai, Gao Yuning
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Multiple normalized solutions for quasi-linear Schr\"odinger equations [PDF]
, 2015 In this paper we prove the existence of two solutions having a prescribed $L^2$-norm for a quasi-linear Schr\"odinger equation. One of these solutions is a mountain pass solution relative to a constraint and the other one a minimum either local or global.
Jeanjean, Louis +2 more
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Nonparaxial dark solitons in optical Kerr media [PDF]
, 2005 We show that the nonlinear equation that describes nonparaxial Kerr propagation, together with the already reported bright-soliton solutions, admits of (1 + 1)D dark-soliton solutions. Unlike their paraxial counterparts, dark solitons can be excited only
Ciattoni, Alessandro +3 more
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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 ...
Bartsch, Thomas, Jeanjean, Louis
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Parabolic Minkowski convolutions of viscosity solutions to fully nonlinear equations [PDF]
, 2019 This paper is concerned with the Minkowski convolution of viscosity solutions of fully nonlinear parabolic equations. We adopt this convolution to compare viscosity solutions of initial-boundary value problems in different domains.
Ishige, Kazuhiro +2 more
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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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