摘要本文引入回火分数p-Laplace(-Δ-λ)ps,讨论了含有对数非线性项的回火分数p-Laplace系统的驻波解.通过极值原理和直接移动平面法,分别研究在全空间和上半空间上驻波解的径向对称性和非存在性. | | 服务 | | | 加入引用管理器 | | E-mail Alert | | RSS | 收稿日期: 2020-06-28 | | 基金资助:国家自然科学基金资助项目(12001344);山西省研究生教育创新项目(2019XY301);山西师范大学研究生科技创新项目(2019XSY025)
| 通讯作者:张丽红,E-mail:zhanglih149@126.com | 作者简介: 王国涛,E-mail:wgt2512@163.com;侯文文,E-mail:lebron_hww@163.com;Ravi P. AGARWAL,E-mail:Ravi.Agarwal@tamuk.edu |
引用本文: | 王国涛, 侯文文, 张丽红, Ravi P. AGARWAL. 带有对数非线性项的回火分数p-Laplace系统的驻波解[J]. 数学学报, 2021, 64(3): 501-514. Guo Tao WANG, Wen Wen HOU, Li Hong ZHANG, Ravi P. AGARWAL. Standing Waves of Tempered Fractional p-Laplace Systems Involving Logarithmic Nonlinearity. Acta Mathematica Sinica, Chinese Series, 2021, 64(3): 501-514. | | | | 链接本文: | http://www.actamath.com/Jwk_sxxb_cn/CN/或 http://www.actamath.com/Jwk_sxxb_cn/CN/Y2021/V64/I3/501 |
[1] Brandle C., Colorado E., de Pablo A., et al., A concave-convex ellipotic problem involving the fractional Laplace, Proc. Roy. Soc. Edinburgh Sect. A, 2013, 143:39-71. [2] Caffarelli L., Silvestre L., An extension problem related to the fractional Laplace, Comm. Partial Differential Equations, 2007, 32:1245-1260. [3] Caffarelli L., Silvestre L., Regularity theory for fully nonlinear integro-differential equations, Comm. Pure Appl. Math., 2009, 62:597-638. [4] Chen W. X., Fang Y. Q., Yang R., Liouville theorems involving the fractional Laplace on a half space, Adv. Math., 2015, 274:167-198. [5] Chen W. X., Li C. M., Methods on Nonlinear Elliptic Equations. AIMS Book Series, Vol. 4:AIMs, Springfield, 2010. [6] Chen W. X., Li C. M., Maximum principles for the fractional p-Laplace and symmetry of solutions, Adv. Math., 2018, 335:735-758. [7] Chen W. X., Li C. M., Li Y., A direct method of moving planes for fractional Laplace, Adv. Math., 2017, 308:404-437. [8] Chen W. X., Li C. M., Ma P., The Fractional Laplace, World Scientific, 2020. [9] Chen W. X., Li C. M., Ou B., Classification of solutions for an integral equation, Comm. Pure Appl. Math., 2006, 59:330-343. [10] Chen W. X., Li C. M., Ou B., Qualitative properties of solutions for an integral equation, Discrete Contin. Dyn. Syst., 2005, 12:347-354. [11] Chen W. X., Zhu J. Y., Indefinite fractional elliptic problem and Liouville theorems, J. Differential Equations, 2016, 260:4758-4785. [12] Chen Y. G., Liu B. Y., Symmetry and non-existence of positive solutions for fractional p-Laplace systems, Nonlinear Anal., 2019, 183:303-322. [13] Csobo E., Genoud F., Ohta M., et al., Stability of standing waves for a nonlinear Klein-Gordon equation with delta potentials, J. Differential Equations, 2019, 268:353-388. [14] Deng W. H., Li B. Y., Tian W. Y., et al., Boundary problems for the fractional and tempered fractional operators, Multiscale Model. Simul., 2018, 16(1):125-149. [15] Dinh V., Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction, Nonlinear Anal., 2020, 190:111589. [16] Duo S. W., Zhang Y. Z., Numerical approximations for the tempered fractional Laplace:error analysis and applications, J. Sci. Comput., 2019, 81(1):569-593. [17] Le P., Ho V., Fractional p-Laplace problems with negative powers in a ball or an exterior domain, J. PseudoDiffer. Oper. Appl., 2020, 11:789-803. [18] Lei Y. Y., Li C. M., Ma C., Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy-Littlewood-Sobolev system of integral equations, Calc. Var. Partial Differential Equations, 2012, 45:43-61. [19] Li C., Deng W. H., Zhao L. J., Well-posedness and numerical algorithm for the tempered fractional ordinary differential equations, Discrete Contin. Dyn. Syst. Ser. B, 2019, 24(4):1989-2015. [20] Liu B. Y., Ma L., Radial symmetry results for fractional Laplace system, Nonlinear Anal., 2016, 146:120-135. [21] Lu G. Z., Zhu J. Y., Symmetry and regularity of extremals of an integral equation related to the HardySobolev inequality, Calc. Var. Partial Differential Equations, 2011, 42:563-577. [22] Ma L., Chen D. Z., A Liouville type theorem for an integral system, Commun. Pure Appl. Anal., 2006, 5:855-859. [23] Ma L., Zhao L., Classification of positive solitary solutions of the nonlinear Choquard equation, Arch. Ration. Mech. Anal., 2010, 195:455-467. [24] Ma L. W., Zhang Z. Q., Symmetry of positive solutions for Choquard equations with fractional p-Laplace, Nonlinear Anal., 2019, 182:248-262. [25] Natali F., Jardoso E. Jr., Orbital stability of periodic standing waves for the logarithmic Klein-Gordon equation, J. Math. Anal. Appl., 2020, 484:123723, 43 pp. [26] Ralf M., Klafter J., The random walk's guide to anomalous diffusion:a fractional dynamics approach, Phys. Rep., 2000, 339(1):1-77. [27] Sun J., Nie D. X., Deng W. H., Algorithm implementation and numerical analysis for the two-dimensional tempered fractional Laplace, preprint, 2018, arXiv:1802.02349. [28] Wang G. T., Ren X. T., Radial symmetry of standing waves for nonlinear fractional Laplace Hardy-Schrödinger systems, 2020, Appl. Math. Lett., 2020, 110:106560, 8 pp. [29] Wang G. T., Ren X. T., Bai Z. B., et al., Radial symmetry of standing waves for nonlinear fractional Hardy-Schrödinger equation, Appl. Math. Lett., 2019, 96:131-137. [30] Wu L. Y., Niu P. Q., Symmetry and nonexistence of positive solutions to fractional p-Laplace equations, Discrete Contin. Dyn. Syst., 2019, 39(3):1573-1583. [31] Zhang L. H., Ahmad B., Wang G. T., et al., Radial symmetry of solution for fractional p-Laplace system, Nonlinear Anal., 2020, 196:111801. [32] Zhang L. H., Hou W. W., Standing waves of nonlinear fractional p-Laplace Schrödinger equation involving logarithmic nonlinearity, Appl. Math. Lett., 2020, 102:106149. [33] Zhang Z. J., Deng W. H., Fan H. T., Finite difference schemes for the tempered fractional Laplace, Numer. Math. Theor. Meth. Appl., 2019, 12(2):492-516. [34] Zhang Z. J., Deng W. H., Karniadakis G. E., A Riesz basis Galerkin method for the tempered fractional Laplace, SIAM J. Numer. Anal., 2018, 56(5):3010-3039. [35] Zhuo R., Chen W. X., Cui X. W., et al., Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplace, Discrete Contin. Dyn. Syst., 2016, 36(2):1125-1141.
|
[1] | 李晓光, 张健, 岳仲涛. 广义Davey——Stewartson系统驻波的强不稳定性[J]. 数学学报, 2018, 61(3): 375-382. | [2] | In Soo BAEK, 李文侠. 广义Cantor函数的不可微点集的维数[J]. Acta Mathematica Sinica, English Series, 2014, 57(5): 939-946. | [3] | 黄业辉, 翁佩萱. 一个具有非局部效应的非线性周期反应扩散方程的渐近形态[J]. Acta Mathematica Sinica, English Series, 2014, 57(5): 1011-1030. | [4] | 邱家亮, 陈宗煊. 高阶亚纯系数非齐次线性微分方程解的零点[J]. Acta Mathematica Sinica, English Series, 2014, 57(4): 727-736. | [5] | 詹华税. 双非线性抛物方程初始迹与Harnack不等式[J]. Acta Mathematica Sinica, English Series, 2014, 57(3): 537-558. | [6] | 杨婉蓉. 3D轴对称Boussinesq方程强解的存在唯一性[J]. Acta Mathematica Sinica, English Series, 2013, 56(5): 637-650. | [7] | 陈美茹, 陈宗煊. 某类均差分的值分布[J]. Acta Mathematica Sinica, English Series, 2012, 55(5): 855-860. | [8] | 陈学勇, 杨茵. 一类趋化性模型行波解的存在性[J]. Acta Mathematica Sinica, English Series, 2012, 55(5): 819-828. | [9] | 陈国旺. 一类N维非线性波动方程的Cauchy问题[J]. Acta Mathematica Sinica, English Series, 2012, 55(5): 797-810. | [10] | 蓝双婷, 陈宗煊. 高阶齐次线性微分方程解的零点[J]. Acta Mathematica Sinica, English Series, 2012, 55(3): 525-534. | [11] | 葛斌, 周庆梅. 由 p-Laplacian 算子导出的半变分不等式的特征值问题[J]. Acta Mathematica Sinica, English Series, 2012, (2): 207-218. | [12] | 裴永珍, 王慧娜, 李长国, 高淑京. 一类具有Logistic增长和Holling II类功能反应的免疫模型[J]. Acta Mathematica Sinica, English Series, 2011, 54(2): 301-312. | [13] | 罗显康, 杨晗. PLn∩PLp空间中MHD方程组强解的存在唯一性及衰减性质[J]. Acta Mathematica Sinica, English Series, 2011, 54(1): 31-40. | [14] | 顾素萍, 罗壮初, 陈化. 高维复域中具非正则奇异性的非线性偏微分方程的形式解[J]. Acta Mathematica Sinica, English Series, 2010, 53(5): 897-904. | [15] | 周文华. 退化抛物型方程弱解的存在性[J]. Acta Mathematica Sinica, English Series, 2010, 53(3): 495-502. |
|
PDF全文下载地址:
http://www.actamath.com/Jwk_sxxb_cn/CN/article/downloadArticleFile.do?attachType=PDF&id=23768
非自治随机FitzHugh-Nagumo系统的随机一致指数吸引子韩宗飞,周盛凡浙江师范大学数学与计算机科学学院金华321004RandomUniformExponentialAttractorforNon-autonomousStochasticFitzHugh-NagumoSystemZongFe ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27半序MengerPM-空间中广义弱压缩映射的最佳逼近点定理吴照奇1,朱传喜1,袁成桂21.南昌大学理学院数学系南昌330031;2.英国斯旺西大学数学系斯旺西SA28PPBestProximityPointTheoremsforGeneralizedWeakContractiveMappingsin ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27完备度量空间中的混沌判定吴小英,陈员龙,王芬广东金融学院金融数学与统计学院广州510521ChaoticCriteriainCompleteMetricSpacesXiaoYingWU,YuanLong,CHENFenWANGSchoolofFinancialMathematicsandStatis ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27空间几何常数与集值非扩张映射的不动点左占飞重庆三峡学院数学与统计学院重庆404100SomeGeometricConstantsandFixedPointsforMultivaluedNonexpansiveMappingsZhanFeiZUODepartmentofMathematicsandSt ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27临界或超临界增长分数阶SchrdingerPoisson方程正解的存在性王文波1,周见文1,李永昆1,李全清21.云南大学数学与统计学院昆明650500;2.红河学院数学学院蒙自661100ExistenceofPositiveSolutionsforFractionalS ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27Banach空间上p-fusion框架的若干等价描述林丽琼1,张云南21.福州大学数学与计算机科学学院福州350108;2.福建师范大学数学与信息学院福州350108SomeEquivalentDescriptionsofp-fusionFramesonBanachSpacesLiQiongLIN1 ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27带有临界增长的分数阶Kirchhoff方程的半经典解赵顺能1,赵富坤21.浙江师范大学数学与计算机科学学院金华321004;2.云南师范大学数学学院昆明650500Semi-classicalSolutionsofFractionalKirchhoff-typeEquationswithCritic ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27加权变指标Herz-Morrey空间上的双线性Hardy算子的交换子王盛荣,徐景实桂林电子科技大学数学与计算科学学院桂林541004CommutatorsofBilinearHardyOperatorsonWeightedHerzMorreySpaceswithVariableExpo ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27加权Bloch空间上复合算子的线性组合张利,楚秀娇南阳师范学院南阳473061LinearCombinationsofCompositionOperatorsonWeightedBlochTypeSpaceLiZHANG,XiuJiaoCHUNanyangNormalUniversity,Nanya ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27bp(2)空间中的等距映射王瑞东,王普天津理工大学理学院天津300384TheIsometryonbp(2)SpaceRuiDongWANG,PuWANGDepartmentofMathematics,TianjinUniversityofTechnology,Tianjin300384,P.R.C ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27
|