Results 11 to 20 of about 2,059,051 (311)
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 solution of a noncooperative elliptic system [PDF]
Differential Equations & Applications, 2013 In this paper, we study the existence of a ground state solution, that is, a non trivial solution with least energy, of a noncooperative semilinear elliptic system on a bounded domain.
Batkam, Cyril Joel
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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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Ground state solutions of scalar field fractional Schrödinger equations [PDF]
Calculus of Variations and Partial Differential Equations, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giovanni Molica Bisci +1 more
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Normalized Ground State Solutions for Nonautonomous Choquard Equations
Frontiers of Mathematics, 2023 In this paper, we study normalized ground state solutions for the following nonautonomous Choquard equation: $$-Δu-λu=\left(\frac{1}{|x|^μ}\ast A|u|^{p}\right)A|u|^{p-2}u,\quad \int_{\mathbb{R}^{N}}|u|^{2}dx=c,\quad u\in H^1(\mathbb{R}^N,\mathbb{R}),$$ where $c>0$, $0< ...
Luo, Huxiao, Wang, Lushun
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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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Ground State Solutions for Kirchhoff Type Quasilinear Equations
Advanced Nonlinear Studies, 2018 Abstract In this paper, we are concerned with quasilinear equations of Kirchhoff type, and prove the existence of ground state signed solutions and sign-changing solutions by using the Nehari method.
Xiangqing Liu, Junfang Zhao
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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 fractional Sobolev critical exponent, 0<s<1, N>2s, G(x,u,v) is a lower order perturbation of ...
Min Liu, Zhijin Wang, Zhenyu Guo
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Ground state and non-ground state solutions of some strongly coupled elliptic systems [PDF]
Transactions of the American Mathematical Society, 2011 We study an elliptic system of the formLu=|v|p−1vLu = \left | v\right |^{p-1} vandLv=|u|q−1uLv=\left | u\right |^{q-1} uinΩ\Omegawith homogeneous Dirichlet boundary condition, whereLu:=−ΔuLu:=-\Delta uin the case of a bounded domain andLu:=−Δu+uLu:=-\Delta u + uin the cases of an exterior domain or the whole spaceRN\mathbb {R}^N.
Bonheure, Denis +2 more
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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} 1
Belliard, Samuel, Faribault, Alexandre
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