具有Hardy位势和临界指数的Kirchhoff型方程的正解
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摘要
根据全空间中半线性椭圆方程的结果,利用伸缩讨论、分析技巧和一些精细的计算,给出了一类具有Hardy位势和临界指数的Kirchhoff型方程的正解.
According to the results of the semilinear elliptic equation in the whole space, by using the rescaling argument, analysis skills and careful calculation, the positive solution for a Kirchhoff type equation with the Hardy potential and critical exponent is obtained.
According to the results of the semilinear elliptic equation in the whole space, by using the rescaling argument, analysis skills and careful calculation, the positive solution for a Kirchhoff type equation with the Hardy potential and critical exponent is obtained.
引文
[1] LIU J,LIU T,PAN H L.A Result on a Non-Autonomous Kirchhoff Type Equation Involving Critical Term [J].Appl Math Lett,2018,85:82-87.
[2] XIE Q L,MA S W,ZHANG X.Bound State Solutions of Kirchhoff Type Problems with Critical Exponent [J].J Differential Equations,2016,261(2):890-924.
[3] AZZOLLINI A.The Elliptic Kirchhoff Equation in RN Perturbed 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 RN Perturbed by a Local Nonlinearity [J].Commun Contemp Math,2015,17(4):1-5.
[5] LIU J,LIAO J F,TANG C L.Positive Solutions for Kirchhoff-Type Equations with Critical Exponent in RN [J].J Math Anal Appl,2015,429(2):1153-1172.
[6] LIU J,YAN Z Q,ZHENG Z B.A Result on a Class of Elliptic Equations Involving Kirchhoff Type Nonlocal Term [J].Comput Math Appl,2017,73(2):355-361.
[7] 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.
[8] 严忠权,柳鸠.具有一般临界增长的自治的Kirchhoff型方程正基态解的存在性 [J].西南师范大学学报(自然科学版),2018,43(2):32-35.
[9] 曾兰,唐春雷.带有临界指数的Kirchhoff型方程正解的存在性 [J].西南大学学报(自然科学版),2016,41(4):29-34.
[10] TERRACINI S.On Positive Entire Solutions to a Class of Equations with a Singular Coefficient and Critical Exponent [J].Adv Differential Equations,1996,1(2):241-264.
[11] FELLI V,TERRACINI S.Elliptic Equations with Multi-Singular Inverse-Square Potentials and Critical Nonlinearity [J].Comm Partial Differential Equations,2006,31(1-3):469-495.
[12] TALENTI G.Best Constant in Sobolev Inequality [J].Ann Mat Pura Appl,1976,110(4):353-372.
[2] XIE Q L,MA S W,ZHANG X.Bound State Solutions of Kirchhoff Type Problems with Critical Exponent [J].J Differential Equations,2016,261(2):890-924.
[3] AZZOLLINI A.The Elliptic Kirchhoff Equation in RN Perturbed 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 RN Perturbed by a Local Nonlinearity [J].Commun Contemp Math,2015,17(4):1-5.
[5] LIU J,LIAO J F,TANG C L.Positive Solutions for Kirchhoff-Type Equations with Critical Exponent in RN [J].J Math Anal Appl,2015,429(2):1153-1172.
[6] LIU J,YAN Z Q,ZHENG Z B.A Result on a Class of Elliptic Equations Involving Kirchhoff Type Nonlocal Term [J].Comput Math Appl,2017,73(2):355-361.
[7] 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.
[8] 严忠权,柳鸠.具有一般临界增长的自治的Kirchhoff型方程正基态解的存在性 [J].西南师范大学学报(自然科学版),2018,43(2):32-35.
[9] 曾兰,唐春雷.带有临界指数的Kirchhoff型方程正解的存在性 [J].西南大学学报(自然科学版),2016,41(4):29-34.
[10] TERRACINI S.On Positive Entire Solutions to a Class of Equations with a Singular Coefficient and Critical Exponent [J].Adv Differential Equations,1996,1(2):241-264.
[11] FELLI V,TERRACINI S.Elliptic Equations with Multi-Singular Inverse-Square Potentials and Critical Nonlinearity [J].Comm Partial Differential Equations,2006,31(1-3):469-495.
[12] TALENTI G.Best Constant in Sobolev Inequality [J].Ann Mat Pura Appl,1976,110(4):353-372.