欢迎您！东篱公司
退出
-
申报数据库
-
立项数据库
-
成果数据库
-
项目获奖数据库
位置：立项数据库 > 立项详情页
中文摘要：
常微分方程边值问题本身具有很强的应用背景，而且又是偏微分方程边值问题研究的基础，有着重要的理论意义和实用价值。当代非线性常微分方程边值问题的研究离不开非线性泛函分析的支持，无论拓扑度理论还是临界点理论，都在近年的研究中得到广泛应用。本课题旨在运用上述两种理论对各类常微分方程边值问题，包括差分方程边值问题和时标上动力系统边值问题进行系统研究，得出有解性和多解性的有效判据，并在理论的应用过程中改进和扩展现有抽象定理的内容和应用领域。三年研究，发表SCI论文90篇，出版著作2本，取得了预期的成果，主要是对带p-Laplace算子的多点边值问题的对称正解和拟对称正解的存在性和迭代方法进行了系统讨论，对多解性作了深入研究，纠正了已有文献中的失误；对二阶和高阶Sturm-Liouville型边值问题的正解存在性给出了有效的判定条件，将这类问题的讨论置于正确的基础之上；研究了时标上动力方程的边值问题，得到了重要的结果；用临界点理论研究带p-Laplace算子常微分方程边值问题，在变分结构的构造等方面有所创新，并得到了理想的结果。
结论摘要：
英文主题词boundary value problem; topological degree; critical point;p-Laplacian; time scale
成果综合统计
期刊论文
会议论文
专利
获奖
著作
期刊论文
MULTIPLE POSITIVE SOLUTIONS FOR A SECOND ORDER STURM-LIOUVILLE BOUNDARY VALUE PROBLEM WITH A p-LAPLA
VARIATIONAL METHODS TO MIXED BOUNDARY VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH A PARA
A necessary and sufficient condition for the existence of positive solutions to a kind of singular t
Existence and nonexistence results of impulsive first-order problem with integral boundary condition
Successive iteration and positive solutions for some second-order three-point p-Laplacian boundary v
Necessary and sufficient conditions for the existence of quasi-symmetric positive solutions of singu
Existence result of second-order differential equations with integral boundary conditions at resonan
Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a h
Existence results of 2m-point boundary value problem of Sturm-Liouville type with sign changing nonl
Successive iteration and positive solutions for a third-order multipoint generalized right-focal bou
Existence and nonexistence of positive solutions for a class of nth-order three-point boundary value
The monotone method for periodic differential equations with the non well-ordered upper and lower so
Positive solutions for one-dimensional p-Laplacian boundary value problems with sign changing nonlin
Existence and iteration of positive solutions to a class of Sturm-Liouville-like p-Laplacian boundar
Exact number of solutions for a class of two-point boundary value problems with one-dimensional p-La
Successive iteration and positive symmetric solutions for some Sturm-Liouville-like four-point p-Lap
Solvability of nonlocal boundary value problems for ordinary differential equation of higher order w
Multiple positive solutions of periodic boundary value problems for second order impulsive different
A symmetric solution of a multipoint boundary value problem with one-dimensional p-Laplacian at reso
Positive solutions for a class of boundary-value problem with integral boundary conditions in Banach
Existence of three positive solutions for m-point boundary-value problems with one-dimensional p-Lap
Multiplicity of symmetric positive solutions for a multipoint boundary value problem with a one-dime
Existence and uniqueness results for nonlinear first-order three-point boundary value problems on ti
Successive iteration and positive pseudo-symmetric solutions for a three-point second-order p-Laplac
Existence and iteration of positive pseudo-symmetric solutions for a three-point second-order p-Lapl
Positive solution of multi-point boundary value problem for the one-dimensional p-laplacian with sin
Existence of triple positive solutions for multi-point boundary value problems with a one dimensiona
Existence of multiple positive solutions for multipoint boundary value problems with a one-dimension
Three positive solutions for multipoint one-dimensional p-Laplacian boundary value problems with dep
The existence of symmetric positive solutions for Sturm-Liouville-like four-point boundary value pro
Existence and iteration of positive solutions for a singular two-point boundary value problem with a
相关项目
葛渭高的项目