Results 11 to 20 of about 1,216,221 (148)
Existence of Multiple Positive Solutions for Choquard Equation with Perturbation [PDF]
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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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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Nodal solutions for the Choquard equation [PDF]
Journal of Functional Analysis, 2016 We consider the general Choquard equations −Δu+u=(Iα∗|u|^p)|u|^(p−2)u where Iα is a Riesz potential. We construct minimal action odd solutions for p∈((N+α)/N,(N+α)/(N−2)) and minimal action nodal solutions for p∈(2,(N+α)/(N−2)).
Van Schaftingen, Jean +2 more
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On Uniqueness for the Generalized Choquard Equation
, 2020 We consider the generalized Choquard equation describing trapped electron gas in three dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. The
George Venkov +3 more
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Multiple solutions of the quasirelativistic Choquard equation [PDF]
Journal of Mathematical Physics, 2012 We prove existence of multiple solutions to the quasi relativistic Choquard equations with a scalar ...
Zongo, Frederic D. Y. +7 more
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The logarithmic Choquard equation : sharp asymptotics and nondegeneracy of the groundstate [PDF]
Journal of Functional Analysis, 2016 We derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation −∆u + au = 1 2π ln 1 |x| * |u| 2 u in R 2 and we establish its nondegeneracy.
Cingolani, Silvia +5 more
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Soliton dynamics for the generalized Choquard equation
Journal of Mathematical Analysis and Applications, 2014 We investigate the soliton dynamics for a class of nonlinear Schrödinger equations with a non-local nonlinear term. In particular, we consider what we call generalized Choquard equation where the nonlinear term is $(|x|^{\theta-N} \star |u|^p) |u|^{p-2}
GHIMENTI, MARCO GIPO +3 more
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Nehari-type ground state solutions for a Choquard equation with doubly critical exponents
Advances in Nonlinear Analysis, 2020 This paper deals with the following Choquard equation with a local nonlinear perturbation:
Chen Sitong, Tang Xianhua, Wei Jiuyang
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A guide to the Choquard equation [PDF]
Journal of Fixed Point Theory and Applications, 2017 We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations −Δu+V(x)u=(|x|−(N−α)∗|u|p)|u|p−2u in RN, and some of its variants and ...
Vitaly Moroz +3 more
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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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