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Ground state solutions for p-biharmonic equations
Electronic Journal of Differential Equations, 2017 In this article we study the p-biharmonic equation $$ \Delta_p^2u+V(x)|u|^{p-2}u=f(x,u),\quad x\in\mathbb{R}^N, $$ where $\Delta_p^2u=\Delta(|\Delta u|^{p-2}\Delta u)$ is the p-biharmonic operator.
Xiaonan Liu +2 more
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A global approach to ground state solutions
Electronic Journal of Differential Equations, 2008 We study radial solutions of semilinear Laplace equations. We try to understand all solutions of the problem, regardless of the boundary behavior. It turns out that one can study uniqueness or multiplicity properties of ground state solutions by ...
Philip Korman
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Ground state solutions for fractional p-Kirchhoff equation
Electronic Journal of Differential Equations, 2022 We study the fractional p-Kirchhoff equation $$ \Big( a+b \int_{\mathbb{R}^N}{\int_{\mathbb{R}^N}} \frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}\, dx\, dy\Big) (-\Delta)_p^s u-\mu|u|^{p-2}u=|u|^{q-2}u, \quad x\in\mathbb{R}^N, $$ where \((-\Delta)_p^s\) is the fractional p-Laplacian operator, a and b are strictly positive real numbers, \(s \in (0,1)\), \(1 < p ...
Lixiong Wang, Haibo Chen, Liu Yang
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Existence of Positive Ground State Solutions for Choquard Systems
Advanced Nonlinear Studies, 2020 We study the existence of positive ground state solution for Choquard systems. In the autonomous case, we prove the existence of at least one positive ground state solution by the Pohozaev manifold method and symmetric-decreasing rearrangement arguments.
Deng Yinbin, Jin Qingfei, Shuai Wei
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Ground state solutions of inhomogeneous Bethe equations [PDF]
SciPost Physics, 2018 The distribution of Bethe roots, solution of the inhomogeneous Bethe equations, which characterize the ground state of the periodic XXX Heisenberg spin-$\frac{1}{2}$ chain is investigated.
S. Belliard, A. Faribault
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Ground State Solutions of Fractional Choquard Problems with Critical Growth
Fractal and Fractional, 2023 In this article, we investigate a class of fractional Choquard equation with critical Sobolev exponent. By exploiting a monotonicity technique and global compactness lemma, the existence of ground state solutions for this equation is obtained.
Jie Yang, Hongxia Shi
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Ground state solutions for a diffusion system
Computers and Mathematics With Applications, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xianhua Tang
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Ground State Solutions to a Critical Nonlocal Integrodifferential System [PDF]
Advances in Mathematical Physics, 2018 Consider the following nonlocal integrodifferential system: LKu+λ1u+μ1u2⁎-2u+Gu(x,u,v)=0 in Ω, LKv+λ2v+μ2v2⁎-2v+Gv(x,u,v)=0 in Ω, u=0, v=0 in RN∖Ω, where LK is a general nonlocal integrodifferential operator, λ1,λ2,μ1,μ2>0, 2⁎≔2N/N-2s is a ...
Min Liu, Zhijing Wang, Zhenyu Guo
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Ground state solutions for the nonlinear Schrödinger–Maxwell equations
Journal of Mathematical Analysis and Applications, 2008 27 ...
A Azzollini, Alessio Pomponio
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Ground state solutions for a quasilinear Kirchhoff type equation [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2016 We study the ground state solutions of the following quasilinear Kirchhoff type equation \[ -\left(1+b\int_{\mathbb{R}^{3}}|\nabla u|^2dx\right)\Delta u + V(x)u-[\Delta(u^2)]u=|u|^{10}u+\mu |u|^{p-1}u,\qquad x\in \mathbb{R}^3, \] where $b\geq 0$ and $\mu$
Hongliang Liu, Haibo Chen, Qizhen Xiao
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