Results 31 to 40 of about 1,216,221 (148)
Linear Barycentric Rational Method for Solving Schrodinger Equation
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 A linear barycentric rational collocation method (LBRCM) for solving Schrodinger equation (SDE) is proposed. According to the barycentric interpolation method (BIM) of rational polynomial and Chebyshev polynomial, the matrix form of the collocation method (CM) that is easy to program is obtained.
Peichen Zhao, Yongling Cheng, Ram Jiwari
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Fractional Choquard equation with critical nonlinearities [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2017 32 pages.
Mukherjee, T., Sreenadh, K.
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Saddle solutions for the fractional Choquard equation [PDF]
Zeitschrift für angewandte Mathematik und Physik, 2022 We study the saddle solutions for the fractional Choquard equation \begin{align*} (-Δ)^{s}u+ u=(K_α\ast|u|^{p})|u|^{p-2}u, \quad x\in \mathbb{R}^N \end{align*} where $s\in(0,1)$, $N\geq 3$ and $K_α$ is the Riesz potential with order $α\in (0,N)$. For every Coxeter group $G$ with rank $1\leq k\leq N$ and $p\in[2,\frac{N+α}{N-2s})$, we construct a $G ...
Ying-Xin Cui, Jiankang Xia
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The Existence of Normalized Solutions for a Nonlocal Problem in ℝ3
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 In this paper, we study the following fractional Schrödinger equation in ℝ3(−Δ)σu − λu = |u|p−2u, in ℝ3 with σ ∈ (0, 1), λ ∈ ℝ and p ∈ (2 + σ, 2 + (4/3)σ). By using the constrained variational method, we show the existence of solutions with prescribed L2 norm for this problem.
Jing Yang, Dimitrios Tsimpis
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An Existence Result for a Generalized Quasilinear Schrödinger Equation with Nonlocal Term
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 In this paper, we consider the following generalized quasilinear Schrödinger equation with nonlocal term −div(g2(u)∇u) + g(u)g′(u)|∇u|2 + V(x)u = λ[|x|−μ∗|u|p]|u|p−2u, x ∈ ℝN, where N ≥ 3, g : ℝ → ℝ+ is a C1 even function, g(0) = 1, g′(s) ≥ 0 is for all s ≥ 0, lim∣s∣→+∞gs/sα−1≔β>0 is for some α > 1, and (α − 1)g(s) ≥ g′(s)s is for all s ≥ 0, 2α ≤ p ...
Quanqing Li +4 more
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Vector Solutions for Linearly Coupled Choquard Type Equations with Lower Critical Exponents
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 The existence, nonexistence, and multiplicity of vector solutions of the linearly coupled Choquard type equations −Δu+V1xu=Iα∗uN+α/Nuα/N−1u+λv,x∈ℝN,−Δv+V2xv=Iα∗vN+α/Nvα/N−1v+λu,x∈ℝN,u,v∈H1ℝN, are proved, where α ∈ (0, N), N ≥ 3, V1(x)V2(x) ∈ L∞(ℝN) are positive functions, and Iα denotes the Riesz potential.
Huiling Wu, Jacopo Bellazzini
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High energy solutions of the Choquard equation
Discrete and Continuous Dynamical Systems, 2018 The present paper is concerned with the existence of positive high energy solution of the Choquard equation. Under certain assumptions, the ground state of Choquard equation can not be achieved. However, by global compactness analysis, we prove that there exists a positive high energy solution.
Cao, Daomin, Li, Hang
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Choquard equations with critical nonlinearities [PDF]
Communications in Contemporary Mathematics, 2019 In this paper, we study the Brezis–Nirenberg type problem for Choquard equations in [Formula: see text] [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text] are the critical exponents in the sense of Hardy–Littlewood–Sobolev inequality and [Formula: see text] is the Riesz ...
Li, Xinfu, Ma, Shiwang
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On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 In the present paper, we consider the following Hamiltonian elliptic system with Choquard’s nonlinear term −Δu+Vxu=∫ΩGvy/x−yβdygv in Ω,−Δv+Vxv=∫ΩFuy/x−yαdyfu in Ω,u=00,v= on ∂Ω,where Ω ⊂ ℝN is a bounded domain with a smooth boundary, 0 < α < N, 0 < β < N, and F is the primitive of f, similarly for G.
Wenbo Wang +3 more
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A Note on a Damped Focusing Inhomogeneous Choquard Equation [PDF]
Zurnal matematiceskoj fiziki, analiza, geometrii, 2021 Summary: This paper is devoted to the focusing inhomogeneous Choquard equation with linear damping: \[ i\dot{u}+\Delta u+iau=-|x|^{-\gamma} (I_\alpha \ast |u|^{p}) |u|^{p-2} u\quad \text{on } \mathbb{R}^N, \] where \(a \geq 0\) and \(0 < \gamma < \operatorname{inf}(N, 2 + \alpha)\).
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