| 非线性四阶周期边值问题正解的存在性和多重性 |
| |
| 引用本文： | 杨和.非线性四阶周期边值问题正解的存在性和多重性[J].大学数学,2011,27(5):33-38. |
| |
| 作者姓名： | 杨和 |
| |
| 作者单位： | 西北师范大学数学与信息科学学院,甘肃兰州,730070 |
| |
| 摘 要： | 研究了四阶两参数常微分方程周期边值问题{u（4）（t）-βu″（t）＋αu（t）=f（t,u（τ（t）））,t∈0,1],u（i）（0）=u（i）（1）,i=1,2,3正解的存在性、多重性和不存在性.在非线性项f（t,u）变号的情形下,用锥上的不动点指数理论证明了该问题至少n个甚至无穷多个正解的存在性,并且获得了该问...
|
| 关 键 词： | 存在性 多重性 无穷多个正解 不存在性 变号非线性项 |
Existence and Multiplicity of Positive Solutions of Nonlinear Fourth-order Periodic Boundary Value Problems |
| |
| YANG He.Existence and Multiplicity of Positive Solutions of Nonlinear Fourth-order Periodic Boundary Value Problems[J].College Mathematics,2011,27(5):33-38. |
| |
| Authors: | YANG He |
| |
| Institution: | YANG He(College of Mathematics and Information Science,Northwest Normal University,Lanzhou,Gansu 730070,China) |
| |
| Abstract: | The existence, multiplicity and nonexistence results of positive solutions are obtained for a nonlinear fourth-order periodic boundary value problem
Under sign-changing nonlinear term f（t,u） , we prove that the problem has at least n and even infinite many positive solutions. At last, a nonexistence theorem has been obtained. The proof relies on fixed point index theorem in eone. |
| |
| Keywords: | existence multiplicity infinite many positive solutions nonexistence sign-changing nonlinear term |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
