测度链上动力方程两点边值问题多解的存在性
Existence of Multiple Solutions for Second Order Second-Point Boundary Value Problems of Dynamics Equation on Time Scale
DOI: 10.12677/PM.2016.64046, PDF,   
作者: 赵梦田*, 李红玉*：山东科技大学数学与系统科学学院，山东 青岛
关键词: 测度链；变号解；特征值；Time Scale； Sign-Changing Solution； Eigenvalue
摘要: 利用格结构下的不动点定理，研究了一类测度链上动力方程的两点边值问题 (1) 其中， ，T是[0，1] 上的闭集， 。 连续，且 。文中结合相应算子的特征值，在非线性项满足次线性条件下，得到此边值问题具有正解，负解和变号解。
Abstract: In this paper, by using the fixed point theorems with lattice structure, we discuss the existence of multiple solutions for the following second-point boundary value problems of dynamics equation on a general time scale. (1) where , Let T be a closed subset of the interval[0,1]  , with , and the function is continuous, with . Combining the eigenvalues of the relevant linear operator, the existence of positive, negative and sign-changing solutions is obtained under the condition that the nonlinear term is sublinear.
文章引用：赵梦田, 李红玉. 测度链上动力方程两点边值问题多解的存在性[J]. 理论数学, 2016, 6(4): 312-317. https://dx.doi.org/10.12677/PM.2016.64046

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