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Existence of Multiple Positive Solutions for Choquard Equation with Perturbation
Advances in Mathematical Physics, 2015 This paper is concerned with the following Choquard equation with perturbation: -Δu+V(x)u=(1/|x|α∗|u|p)|u|p-2u+g(x), u∈H1(RN), where N≥3, α∈(0,N), and 2-(α/N)
Tao Xie, Lu Xiao, Jun Wang
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Existence of Multispike Positive Solutions for a Nonlocal Problem in ℝ3
Advances in Mathematical Physics, 2020 In this paper, we study the following nonlinear Choquard equation −ϵ2Δu+Kxu=1/8πϵ2∫ℝ3u2y/x−ydyu,x∈ℝ3, where ϵ>0 and Kx is a positive bounded continuous potential on ℝ3.
Jing Yang, Qiuxiang Bian, Na Zhao
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Existence of nontrivial weak solutions for a quasilinear Choquard equation [PDF]
Journal of Inequalities and Applications, 2018 We are concerned with the following quasilinear Choquard equation: −Δpu+V(x)|u|p−2u=λ(Iα∗F(u))f(u)in RN,F(t)=∫0tf(s)ds, $$ -\Delta_{p} u+V(x)|u|^{p-2}u=\lambda\bigl(I_{\alpha} \ast F(u)\bigr)f(u) \quad \text{in } \mathbb {R}^{N}, \qquad F(t)= \int_{0}^{t}
Jongrak Lee +3 more
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The Choquard Equation with Weighted Terms and Sobolev-Hardy Exponent
Journal of Function Spaces, 2018 We study a nonlinear Choquard equation with weighted terms and critical Sobolev-Hardy exponent. We apply variational methods and Lusternik-Schnirelmann category to prove the multiple positive solutions for this problem.
Yanbin Sang, Xiaorong Luo, Yongqing Wang
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Remarks on damped Schrödinger equation of Choquard type [PDF]
Opuscula Mathematica, 2021 This paper is devoted to the Schrödinger-Choquard equation with linear damping. Global existence and scattering are proved depending on the size of the damping coefficient.
Lassaad Chergui
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Advances in Mathematical Physics, Volume 2023, Issue 1, 2023., 2023 This article is concerned with the initial‐value problem of a Schrödinger–Hartree equation in the presence of anisotropic partial/whole harmonic confinement. First, we get a sharp threshold for global existence and finite time blow‐up on the ground state mass in the L2‐critical case. Then, some new cross‐invariant manifolds and variational problems are
Min Gong, Hui Jian, Igor Freire
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Advanced Nonlinear Studies, 2021 In this paper, we investigate the non-autonomous Choquard ...
Li Yong-Yong, Li Gui-Dong, Tang Chun-Lei
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Existence of Two Solutions for a Critical Elliptic Problem with Nonlocal Term in ℝ4
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In this paper, we prove the existence of two positive solutions for a critical elliptic problem with nonlocal term and Sobolev exponent in dimension four.
Khadidja Sabri +4 more
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Advances in Mathematical Physics, Volume 2022, Issue 1, 2022., 2022 In this paper, we consider the following fourth order elliptic Kirchhoff‐type equation involving the critical growth of the form Δ2u−a+b∫ℝN∇u2dxΔu+Vxu=Iα∗Fufu+λu2∗∗−2u,in ℝN,u∈H2ℝN, where a > 0, b ≥ 0, λ is a positive parameter, α ∈ (N − 2, N), 5 ≤ N ≤ 8, V : ℝN⟶ℝ is a potential function, and Iα is a Riesz potential of order α.
Li Zhou, Chuanxi Zhu, Sergey Shmarev
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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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