一类渐近3-线性Kirchhoff型方程的正基态解
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摘要
采用变分方法研究了一类渐近3-线性Kirchhoff型方程.利用极小作用原理,得到非零非负解的存在性.最后利用强极大值原理,得到了一个正的基态解.
In this paper, we have mainly studied a class of asymptotically 3-linear Kirchhoff-type equations by variational method. Using the principle of minimal action, the existence of non-zero and non-negative solution is obtained. Finally, a positive ground state solution is obtained by using the strong maximum principle.
In this paper, we have mainly studied a class of asymptotically 3-linear Kirchhoff-type equations by variational method. Using the principle of minimal action, the existence of non-zero and non-negative solution is obtained. Finally, a positive ground state solution is obtained by using the strong maximum principle.
引文
[1] KIRCHHOFF G.Mechanik [M].Teubner:Leipzig,1883.
[2] SUN Y J,LIU X.Existence of Positive Solutions for Kirchhoff Type Problems with Critical Exponent [J].J Partial Differ Equ,2012,25(2):187-198.
[3] LEI C Y,LIU G S,GUO L T.Multiple Positive Solutions for a Kirchhoff Type Problem with a Critical Nonlinearity [J].Nonlinear Analysis Real World Applications,2016,31:343-355.
[4] NAIMEN D.The Critical Problem of Kirchhoff Type Elliptic Equations in Dimension Four [J].J Differential Equations,2014,257(4):1168-1193.
[5] LIAO J F,ZHANG P,LIU J,et al.Existence and Multiplicity of Positive Solutions for a Class of Kirchhoff Type Problems at Resonance [J].Discrete and Continuous Dynamical Systems,2016,9(6):1959-1974.
[6] PERERA K,ZHANG Z T.Nontrivial Solutions of Kirchhoff-Type Problems Via the Yang Index [J].J Differential Equations,2006,221(1):246-255.
[7] 廖家锋,张鹏,唐春雷.一类渐近4次线性Kirchhoff方程的多解性 [J].西南师范大学学报(自然科学版),2014,39(8):19-22.
[8] 赵荣胜,唐春雷.一类Kirchhoff型方程解的多重性 [J].西南大学学报(自然科学版),2015,37(2):60-64.
[9] 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.
[10] 丁瑶,廖家锋.一类带临界指数的非齐次Kirchhoff型方程正解的存在性 [J].西南师范大学学报(自然科学版),2015,40(12):17-21.
[11] XIE Q L,WU X P,TANG C L.Existence and Multiplicity of Solutions For Kirchhoff Type Problem with Critical Exponent [J].Commun Pure Appl Anal,2013,12(6):2773-2794.
[2] SUN Y J,LIU X.Existence of Positive Solutions for Kirchhoff Type Problems with Critical Exponent [J].J Partial Differ Equ,2012,25(2):187-198.
[3] LEI C Y,LIU G S,GUO L T.Multiple Positive Solutions for a Kirchhoff Type Problem with a Critical Nonlinearity [J].Nonlinear Analysis Real World Applications,2016,31:343-355.
[4] NAIMEN D.The Critical Problem of Kirchhoff Type Elliptic Equations in Dimension Four [J].J Differential Equations,2014,257(4):1168-1193.
[5] LIAO J F,ZHANG P,LIU J,et al.Existence and Multiplicity of Positive Solutions for a Class of Kirchhoff Type Problems at Resonance [J].Discrete and Continuous Dynamical Systems,2016,9(6):1959-1974.
[6] PERERA K,ZHANG Z T.Nontrivial Solutions of Kirchhoff-Type Problems Via the Yang Index [J].J Differential Equations,2006,221(1):246-255.
[7] 廖家锋,张鹏,唐春雷.一类渐近4次线性Kirchhoff方程的多解性 [J].西南师范大学学报(自然科学版),2014,39(8):19-22.
[8] 赵荣胜,唐春雷.一类Kirchhoff型方程解的多重性 [J].西南大学学报(自然科学版),2015,37(2):60-64.
[9] 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.
[10] 丁瑶,廖家锋.一类带临界指数的非齐次Kirchhoff型方程正解的存在性 [J].西南师范大学学报(自然科学版),2015,40(12):17-21.
[11] XIE Q L,WU X P,TANG C L.Existence and Multiplicity of Solutions For Kirchhoff Type Problem with Critical Exponent [J].Commun Pure Appl Anal,2013,12(6):2773-2794.