《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (2): 84-88.doi: 10.6040/j.issn.1671-9352.0.2018.155
• • 上一篇
吴忆佳,成荣*
WU Yi-jia, CHENG Rong*
摘要: 讨论一类具有变号位势的Schrödinger方程的无穷多非平凡解的存在性,其非线性项具有超二次的增长条件,建立了此类方程的无穷多解的存在性结果。结果推广了已有的结论。
中图分类号:
[1] LI Yi. Remarks on a semilinear elliptic equation on RN[J]. Journal of Differential Equations, 1988, 74(1):34-49. [2] RABINOWITZ P H. On a class of nonlinear Schrödinger equations[J]. Zeitschrift für angewandte Mathematik und Physik ZAMP, 1992, 43(2):270-291. [3] LIU Xiangqing,HUANG Yisheng. Sign-changing solutions for a class of nonlinear Schrödinger equations[J]. Bulletin of the Australian Mathematical Society, 2009, 80(2):294-305. [4] CAO Daomin, LI Shuanglong, LUO Peng. Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations[J]. Calculus of Variations and Partial Differential Equations, 2015, 54(4):4037-4063. [5] JUÁREZ HURTADO E, MIYAGAKI O H, RODRIGUES R S. Existence and multiplicity of solutions for a class of elliptic equations without Ambrosetti-Rabinowitz type conditions[J]. Journal of Dynamics and Differential Equations, 2018, 30(2):405-432. [6] CHEN Huyuan, FELMER P, QUAAS A. Large solution to elliptic equations involving fractional Laplacian[J]. Annales De Linstitut Henri Poincaré, 2015, 32(6):1199-1228. [7] CHEN Huyuan, VÉRON L. Semilinear fractional elliptic equations involving measures[J]. Journal of Differential Equations, 2014, 257(5):1457-1486. [8] BARTSCH T, JEANJEAN L, SOAVE N. Normalized solutions for a system of coupled cubic Schrödinger equations on R3[J]. Journal De Mathematiques Pures Et Appliquees, 2016, 106(4):583-614. [9] BARTSCH T, SOAVE N. A natural constraint approach to normalized solutions on nonlinear Schrödinger equations and systems[J]. Journal of Functional Analysis, 2017, 272(12):4998-5037. [10] TANG Xianhua. Infinitely many solutions for semilinear Schrödinger equations with sign-changing potential and nonlinearity[J]. Journal of Mathematical Analysis and Applications, 2013, 401(1):407-415. [11] ZHANG Qingye, XU Bin. Multipicity of solutions for a class of semilinear Schrödinger equations with sign-changing potential[J]. Journal of Mathematical Analysis and Applications, 2001, 377(2):834-840. [12] ZOU Wenming. Variant fountain theorems and their applications[J]. Manuscripta Mathematica, 2001, 104(3):343-358. [13] RABINOWITZ P H. Minimax methods in critical point theory with applications to differential equations[J]. Conference Board of the Mathematical Sciences, 1986, 65:1-100. |
[1] | 张申贵. 四阶变指数椭圆方程Navier边值问题的多解性[J]. 山东大学学报(理学版), 2018, 53(2): 32-37. |
[2] | 黄爱玲,林帅. 局部量子Bernoulli噪声意义下的随机Schrödinger方程的有限维逼近[J]. 山东大学学报(理学版), 2017, 52(12): 67-71. |
[3] | 江静,高庆龄,张克玉. 时标上二阶Dirichlet边值问题弱解的存在性[J]. 山东大学学报(理学版), 2016, 51(6): 99-103. |
[4] | 张申贵. 带p(x)-调和算子的Kirchhoff型方程的多重解[J]. 山东大学学报(理学版), 2016, 51(10): 48-53. |
[5] | 孙国伟, 买阿丽. 一类二阶非线性差分方程同宿解的多解性[J]. 山东大学学报(理学版), 2015, 50(05): 51-54. |
[6] | 王萍莉, 石东洋. Schrödinger方程双线性元的 超收敛分析和外推[J]. 山东大学学报(理学版), 2014, 49(10): 66-71. |
[7] | 张申贵. 局部超线性p-基尔霍夫方程的多重解[J]. 山东大学学报(理学版), 2014, 49(05): 61-68. |
[8] | 张国威1,陈昂2. 初始例函数的游荡域的无穷连通性[J]. 山东大学学报(理学版), 2014, 49(04): 70-73. |
[9] | 张申贵. 一类超线性p(x)-调和方程的无穷多解[J]. J4, 2012, 47(10): 116-120. |
[10] | 张申贵. 一类非自治二阶系统的多重周期解[J]. J4, 2011, 46(11): 64-69. |
[11] | 陆瑶1,李德生2,杨洋1. 非线性SchrÖdinger方程的Fourier谱逼近[J]. J4, 2011, 46(1): 119-126. |
[12] | 朱海霞1,晏世雷2. 随机晶场作用的Blume-Capel模型的相图研究[J]. J4, 2011, 46(1): 51-55. |
[13] | . 用变分法研究势场V(r)中存在束缚态的条件[J]. J4, 2009, 44(5): 62-66. |
[14] | 许万银. 一类拟线性Neumann问题的多重解[J]. J4, 2009, 44(10): 39-42. |
[15] | 张懿彬 . 带指数增长型Neumann边界条件的Laplace方程解的存在性[J]. J4, 2008, 43(3): 48-53 . |
|