|
|
- 2018
一类次线性分数阶Schr？dinger方程的无穷多解
|
Abstract:
$研究了如下的分数阶Schr？dinger方程：$
{{\left( -\Delta \right)}^{s}}u+V\left( x \right)u=f\left( x,u \right)\ \ \ \ \ x\in {{\mathbb{R}}^{N}}
$
其中N≥3,V是变号位势,f是次线性的.运用对称山路引理,得到了该方程无穷多解的存在性.$
$The following fractional Schr？dinger equation is studied
$
{{\left( -\Delta \right)}^{s}}u+V\left( x \right)u=f\left( x,u \right)\ \ \ \ \ x\in {{\mathbb{R}}^{N}}
$
where N≥3, V is an indefinite potential and f satisfies sublinear growth. The existence of infinitely many solutions is obtained by using the variant symmetric mountain lemma.
| [1] | LI L, ZHONG X. Infinitely Many Small Solutions for the Kirchhoff Equation with Local Sublinear Nonlinearities[J]. J Math Anal Appl, 2016, 435(1): 955-967. DOI:10.1016/j.jmaa.2015.10.075 |
| [2] | KHOUTIR S, CHEN H B. Existence of Infinitely Many High Energy Solutions for a Fractional Schr？dinger Equation in ${{\mathbb{R}}^{N}}$ [J]. Appl Math Lett, 2016, 61(2): 156-162. |
| [3] | BIN G. Multiple Solutions of Nonlinear Schr？dinger Equation with the Fractional Laplacian[J]. Nonlinear Anal, 2016, 30: 236-247. DOI:10.1016/j.nonrwa.2016.01.003 |
| [4] | ZHANG W, TANG X H, ZHANG J. Infinitely Many Radial and Non-Radial Solutions for a Fractional Schr？dinger Equation[J]. Comput Math Appl, 2016, 71(3): 737-747. DOI:10.1016/j.camwa.2015.12.036 |
| [5] | 刘晓琪, 欧增奇. 一类Kirchhoff型分数阶p-拉普拉斯方程无穷解的存在性[J]. 西南大学学报(自然科学版), 2017, 39(4): 70-75. |
| [6] | NEZZA E D, PALATUCCI G, VALDINOCI E. Hitchhiker's Guide to the Fractional Sobolev Spaces[J]. Bull Sci Math, 2011, 136(5): 521-573. |
| [7] | TENG K M. Multiple Solutions for a Class of Fractional Schr？dinger Equations in ${{\mathbb{R}}^{N}}$ [J]. Nonlinear Anal, 2015, 21(21): 76-86. |
