渐近线性的Kirchhoff类方程变号解的存在性
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摘要
研究了全空间上一类径向对称的在无穷远点是渐近线性非线性项的自治的Kirchhoff方程,在适当条件下证明了Kirchhoff方程等价一个椭圆系统.再用各种分析技巧,得到了方程径向变号解的存在性结果。
In this paper,a class of radially symmetric autonomous Kirchhoff equations with asymptotic linearity at infinity is studied.Under the suitable conditions,we prove that the Kirchhoff equation is proved to be equivalent to the elliptic system.Furthermore,by using some analysis techniques,the existence result of a sign-changing solution is obtained.
In this paper,a class of radially symmetric autonomous Kirchhoff equations with asymptotic linearity at infinity is studied.Under the suitable conditions,we prove that the Kirchhoff equation is proved to be equivalent to the elliptic system.Furthermore,by using some analysis techniques,the existence result of a sign-changing solution is obtained.
引文
[1] MAIA L A,MIYAGAKI O H,SOARES S H M.A sign-changing solution for an asymptotically linear Schr?dinger equation[J].Proceedings of the Edinburgh Mathematics Society,2015,58(3):697-716.
[2] BENSEDIC A,BOUCHEKIF M.On an elliptic equation of Kirchhoff-type with a potential asymptotically linear at infinity[J].Mathematical and Computer Modeling,2009,49(5-6):1089-1096.
[3] LI L,SUN J J.Existence and multiplicity of solutions for the Kirchhoff equations with asymptotically linear Nonlinearities[J].Nonlinear Analysis:Real Word Applications,2015,26:391-399.
[4] WU K,ZHOU F.Nodal solutions for a Kirchhoff type problem in RN[J].Applied Mathematics Letters,2019,88:58-63.
[5] 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.
[6] LIU J,LIAO J F,TANG C L.Positive solutions of Kirchhoff-type equations with critical exponent in RN[J].J Math Anal Appl,2015,429(2):1153-1172.
[7] FAN H .Multiple positive solutions for Kirchhoff-type problems in R3 involving critical Sobolev exponents[J].Z Angew Math Phys,2016,67(5):129.
[8] 丁凌,汪继秀,肖氏武.全空间上具有临界指数的Kirchhoff类方程无穷多个正解的存在性[J].南昌大学学报(理科版),2017,41(5):414-417.
[9] 丁凌,汪继秀,张丹丹.全空间上具有临界指数的Kirchhoff类方程两个正解的存在性[J].四川大学学报(自然科学版),2018,55(3):457-461.
[10] 刘丽,孟娟娟,毛安民.次线性基尔霍夫问题的无穷多解[J].南昌大学学报(理科版),2017,41(5):423-427.
[2] BENSEDIC A,BOUCHEKIF M.On an elliptic equation of Kirchhoff-type with a potential asymptotically linear at infinity[J].Mathematical and Computer Modeling,2009,49(5-6):1089-1096.
[3] LI L,SUN J J.Existence and multiplicity of solutions for the Kirchhoff equations with asymptotically linear Nonlinearities[J].Nonlinear Analysis:Real Word Applications,2015,26:391-399.
[4] WU K,ZHOU F.Nodal solutions for a Kirchhoff type problem in RN[J].Applied Mathematics Letters,2019,88:58-63.
[5] 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.
[6] LIU J,LIAO J F,TANG C L.Positive solutions of Kirchhoff-type equations with critical exponent in RN[J].J Math Anal Appl,2015,429(2):1153-1172.
[7] FAN H .Multiple positive solutions for Kirchhoff-type problems in R3 involving critical Sobolev exponents[J].Z Angew Math Phys,2016,67(5):129.
[8] 丁凌,汪继秀,肖氏武.全空间上具有临界指数的Kirchhoff类方程无穷多个正解的存在性[J].南昌大学学报(理科版),2017,41(5):414-417.
[9] 丁凌,汪继秀,张丹丹.全空间上具有临界指数的Kirchhoff类方程两个正解的存在性[J].四川大学学报(自然科学版),2018,55(3):457-461.
[10] 刘丽,孟娟娟,毛安民.次线性基尔霍夫问题的无穷多解[J].南昌大学学报(理科版),2017,41(5):423-427.