一类拟线性重调和方程基态解的存在性
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摘要
用变分法、变量替换和Nehari流形方法,在非线性项满足一定增长性条件的情形下,通过构造Nehari流形并对流形性质的证明,得到一类拟线性重调和方程基态解的存在性.
Using the variational method,variable substitution and the Nehari manifold method,we obtained the existence of ground state solution for a class of quasilinear biharmonic equations by constructing the Nehari manifold and proving the properties of manifold when the nonlinearity term satisfied certain growth conditions.
Using the variational method,variable substitution and the Nehari manifold method,we obtained the existence of ground state solution for a class of quasilinear biharmonic equations by constructing the Nehari manifold and proving the properties of manifold when the nonlinearity term satisfied certain growth conditions.
引文
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[2]COLIN M,JEANJEAN L.Solutions for a Quasilinear Schr9dinger Equation:Dual Approach[J].Nonlinear Anal,2004,56(2):213-226.
[3]MIYAGAKI O H,MOREIRA S I,PUCCI P.Multiplicity of Nonnegative Solutions for Quasilinear Schr9dinger Equations[J].J Math Anal Appl,2016,434(1):939-955.
[4]WANG Youjun,LI Zhouxin,ABDELGADIR A A.On Singular Quasilinear Schr9dinger Equations with Critical Exponents[J].Math Meth Appl Sci,2017,40(14):5095-5108.
[5]SONG Hongxue,CHEN Caisheng,YAN Qinglun.Infinitely Many Solutions for Quasilinear Schr9dinger Equation with Critical Exponential Growth in瓗N[J].J Math Anal Appl,2016,439(2):575-593.
[6]WANG Youjun.Multiplicity of Solutions for Singular Quasilinear Schr9dinger Equations with Critical Exponents[J].J Math Anal Appl,2018,458(2):1027-1043.
[7]RUIZ D,SICILIANO G.Existence of Ground States for a Modified Nonlinear Schr9dinger Equation[J].Nonlinearity,2010,23(5):1221-1233.
[8]BRIZHIK L,EREMKO A,PIETTE B,et al.Static Solutions of a D-Dimensional Modified Nonlinear Schr9dinger Equation[J].Nonlinearity,2003,16(4):1481-1497.
[9]KURIHARA S.Large-Amplitude Quasi-solitons in Superfluid Films[J].J Phys Soc Japan,1981,50(10):3262-3267.
[10]HARTMANN B,ZAKRZEWSKI W J.Electrons on Hexagonal Lattices and Applications to Nanotubes[J].Phys Rev B,2003,68(18):184302-1-184302-9.
[11]FIGUEIREDO G M,SEVERO U B,SICILIANO G.Multiplicity of Positive Solutions for a Quasilinear Schr9dinger Equation with an Almost Critical Nonlinearity[J/OL].2018-01-25.https://arxiv.org/pdf/1801.08516.pdf.