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GROUND STATE SOLUTIONS OF NEHARI-POHOZAEV TYPE FOR A FR ACTIONAL SCHRODINGER-POISSON SYSTEM WITH CRITICAL GROWTH 被引量:1
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作者 Wentao HUANG Li WANG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第4期1064-1080,共17页
We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 0<s,t<1,2s+2t>3 and 2s=6/3-2s is the critical ... We study the following nonlinear fractional Schrodinger-Poisson system with critical growth:{(-△)sμ+μ+φμ=f(μ)+|μ|2s-2μ,x∈R3.(-△)tφ=μ2x∈R3,(0.1)where 0<s,t<1,2s+2t>3 and 2s=6/3-2s is the critical Sobolev exponent in 1R3.Under some more general assumptions on f,we prove that(0.1)admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold. 展开更多
关键词 fractional Schrodinger-Poisson system nehari-pohozaev manifold ground state solutions critical growth
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带有一般位势的分数阶薛定谔-泊松系统Nehari-Pohozaev类型基态解的存在性
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作者 刘珂 杜新生 《曲阜师范大学学报(自然科学版)》 CAS 2020年第3期25-34,共10页
研究了下述带有一般位势的分数阶薛定谔-泊松系统的基态解的存在问题(-Δ)su+V(x)u+φu=f(u),inR^3,(-Δ)tφ=u 2,inR^3,其中(-Δ)s和(-Δ)t代表了分数阶拉普拉斯,0<s≤t<1而且2s+2t>3,位势V(x)弱可微,f∈C(ℝ,ℝ).在位势函数V(x... 研究了下述带有一般位势的分数阶薛定谔-泊松系统的基态解的存在问题(-Δ)su+V(x)u+φu=f(u),inR^3,(-Δ)tφ=u 2,inR^3,其中(-Δ)s和(-Δ)t代表了分数阶拉普拉斯,0<s≤t<1而且2s+2t>3,位势V(x)弱可微,f∈C(ℝ,ℝ).在位势函数V(x)以及非线性项f(u)满足一定假设下,利用Jeanjean单调技巧和全局紧性引理,得到了该问题Nehari-Pohozaev型基态解的存在性. 展开更多
关键词 分数阶薛定谔-泊松问题 nehari-pohozaev类型基态解 全局紧性引理
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p-Laplace问题规范解的存在性
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作者 刘炳钊 李园园 《洛阳理工学院学报(自然科学版)》 2024年第2期71-78,共8页
对一类包含p-Laplace算子的非线性问题规范解的存在性进行研究,用极小化方法研究了当微分方程连续且满足某些适当的Berestycki-Lions类型条件下,Nehari-Pohozaev流形的正规范解。
关键词 p-Laplace问题 规范解 nehari-pohozaev流形 最小化方法
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四阶拟线性椭圆型方程的基态解
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作者 胡蝶 张齐 《数学理论与应用》 2021年第2期39-56,共18页
本文研究四阶拟线性椭圆型方程:{△^(2)u−△u+V(x)u−1/2u△(u^(2))=f(u),x∈R^(N),u∈H^(2)(R^(N)),其中△^(2):=△(△)为双调和算子,2<N≤6,我们证明上述方程具有Nehari-Pohozaev型基态解.
关键词 四阶拟线性椭圆型方程 Pohozaev型基态解 变分法
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Ground state solutions for a class of fractional Kirchhoff equations with critical growth 被引量:2
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作者 Xiaoming He Wenming Zou 《Science China Mathematics》 SCIE CSCD 2019年第5期853-890,共38页
In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parame... In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parameter,■ , and V : R^3→ R is a continuous potential function. For suitable assumptions on V, we show the existence of a positive ground state solution, by using the methods of the Pohozaev-Nehari manifold, Jeanjean's monotonicity trick and the concentration-compactness principle due to Lions(1984). 展开更多
关键词 FRACTIONAL KIRCHHOFF EQUATIONS ground state solutions Pohozaev-Nehari MANIFOLD critical SOBOLEV EXPONENT
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Flat Solutions of Some Non-Lipschitz Autonomous Semilinear Equations May be Stable for N≥3
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作者 Jesús Ildefonso DIAZ Jesús HERNaNDEZ Yavdat IL'Y ASOV 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2017年第1期345-378,共34页
The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equat... The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N = 1, 2 and they can be stable for N ≥ 3 for suitable values of the involved exponents. 展开更多
关键词 Semilinear elliptic and parabolic equation Strong absorption Spectral problem Nehari manifolds Pohozaev identity Flat solution Linearized stability Lyapunov function Global instability
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