Cylindrical Solutions and Ground State Solutions to Weighted Kirchhoff Equations

被引：0
作者：
Zupei Shen
Jianshe Yu
机构：
[1] Guangdong University of Finance,School of Financial Mathematics and Statistics
[2] Guangzhou University,Center for Applied Mathematics
来源：
The Journal of Geometric Analysis | 2022年 / 32卷
关键词：
Kirchhoff equation; Cylindrical solution; Ground state solution; Concentration Compactness Principle; 35J10; 35J20; 35J60;
D O I：
暂无
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学科分类号：
摘要：
We analyze the existence and non-existence of cylindrical solutions as well as ground state solutions to a class of Kirchhoff-type problems with critical Sobolev exponent, subcritical Sobolev exponent, and critical Sobolev–Hardy exponent. To the best of our knowledge, this is the first time to study the existence of cylindrically symmetric solutions to the Kirchhoff equations in the literature.
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[1]  
Arosio A(1996)On the well-posedness of the Kirchhoff string Trans. Am. Math. Soc. 348 305-330
[2]  
Panizzi S(2002)A Sobolev–Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics Arch. Ration. Mech. Anal. 163 259-293
[3]  
Badiale M(1992)Global solvability for the degenerate Kirchhoff equation with real analytic data Invent. Math. 108 247-262
[4]  
Tarantello G(2015)Existence and asymptotic behavior of nodal solutions for the Kirchhoff-type problems in J. Funct. Anal. 269 3500-3527
[5]  
D’Ancona P(2019)Homoclinic solutions of discrete nonlinear systems via variational method J. Appl. Anal. Comput. 9 271-294
[6]  
Spagnolo S(2019)Bound state solutions for some non-autonomous asymptotically cubic Schrödinger–Poisson systems Z. Angew. Math. Phys. 70 50-2032
[7]  
Deng Y(2013)Multiple solutions for a quasilinear Schrödinger equation J. Differ. Equ. 254 2015-979
[8]  
Peng S(2014)Existence and concentration result for the Kirchhoff type equations with general nonlinearities Arch. Ration. Mech. Anal. 213 931-60
[9]  
Shuai W(2015)Existence of a nodal solution with minimal energy for a Kirchhoff equation Math. Nachr. 288 48-600
[10]  
Erbe L (2014)Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in J. Differ. Equ. 257 566-2005
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