具有一般临界增长的自治的Kirchhoff型方程正基态解的存在性
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摘要
研究了一类具有一般临界增长的自治的Kirchhoff型方程.利用Schr9dinger方程中的结果和伸缩讨论以及Pohozaev等式得到方程具有一个正基态解并且该解还是径向对称的.
In the paper,a class of autonomous Kirchhoff-type equation involving the general critical growth has been studied.By using the result on Schrodinger equation,rescaling argument and Pohozaev equality,equation has been obtained with a positive ground state solution which is radically symmetric.
In the paper,a class of autonomous Kirchhoff-type equation involving the general critical growth has been studied.By using the result on Schrodinger equation,rescaling argument and Pohozaev equality,equation has been obtained with a positive ground state solution which is radically symmetric.
引文
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[5]HE Y,LI G.Standing Waves for a Class of Kirchhoff Type Problems in R3 Involving Critical Sobolev Exponents[J].Calc Var Partial Differential Equations,2015,54(3):3067-3106.
[6]LI G,YE H.Existence of Positive Ground State Solutions for the Nonlinear Kirchhoff Type Equations in R3[J].J Differential Equations,2014,257(2):566-600.
[7]LIU J,LIAO J F,TANG C L.The Existence of a Ground-State Solution for a Class of Kirchhoff-Type Equations in RN[J].Proc Roy Soc Edinburgh Sect A,2016,146(2):371-391.
[8]LIU Z,GUO S.On Ground States for the Kirchhoff-Type Problem with a General Critical Nonlinearity[J].J Math Anal Appl,2015,426(1):267-287.
[9]LU S S.An Autonomous Kirchhoff-Type Equation with General Nonlinearity in RN[J].Nonlinear Anal Real World Appl,2017,34:233-249.
[10]刘选状,吴行平,唐春雷.一类带有临界指数增长项的Kirchhoff型方程正的基态解的存在性[J].西南大学学报(自然科学版),2015,37(6):54-59.
[2]LIU J,LIAO J F,TANG C L.Ground State Solution for a Class of Schr9dinger Equations Involving General Critical Growth Term[J].Nonlinearity,2017,30(3):899-911.
[3]AZZOLLINI A.The Elliptic Kirchhoff Equation in RNPerturbed by a Local Nonlinearity[J].Differential Integral Equations,2012,25(5-6):543-554.
[4]AZZOLLINI A.A Note on the Elliptic Kirchhoff Equation in RNPerturbed by a Local Nonlinearity[J].Commun Contemp Math,2015,17(4):1-5.
[5]HE Y,LI G.Standing Waves for a Class of Kirchhoff Type Problems in R3 Involving Critical Sobolev Exponents[J].Calc Var Partial Differential Equations,2015,54(3):3067-3106.
[6]LI G,YE H.Existence of Positive Ground State Solutions for the Nonlinear Kirchhoff Type Equations in R3[J].J Differential Equations,2014,257(2):566-600.
[7]LIU J,LIAO J F,TANG C L.The Existence of a Ground-State Solution for a Class of Kirchhoff-Type Equations in RN[J].Proc Roy Soc Edinburgh Sect A,2016,146(2):371-391.
[8]LIU Z,GUO S.On Ground States for the Kirchhoff-Type Problem with a General Critical Nonlinearity[J].J Math Anal Appl,2015,426(1):267-287.
[9]LU S S.An Autonomous Kirchhoff-Type Equation with General Nonlinearity in RN[J].Nonlinear Anal Real World Appl,2017,34:233-249.
[10]刘选状,吴行平,唐春雷.一类带有临界指数增长项的Kirchhoff型方程正的基态解的存在性[J].西南大学学报(自然科学版),2015,37(6):54-59.