非线性Volterra-Stieltjes型积分方程解的存在性

根据非紧性测度以及凸幂凝聚算子的不动点定理,研究一类更具一般性的非线性Volterra-Stieltjes型积分方程解的存在性.由于非线性项中含有非线性积分算子,相对于线性积分算子,所得结论推广和丰富了已有的一些结果.

非线性Volterra-Stieltjes积分方程的解

利用Schauder不动点定理和饱和解的理论,研究下列非线性Volterra- Stieltjes积分方程x(t)=h(t)+∫_0~t u(t,s,x(s))d_sg(t,s).在适当的条件下,证明了上述方程在[0,+∞)上有连续解.

Volterra-Stieltjes型泛函积分方程解的存在性及渐近行为

利用非紧性测度理论和Schauder不动点定理,该文研究了无界区间上Volterra-Stieltjes型泛函积分方程解的存在性和渐近行为.作为应用,并给出了一些例子来验证主要结论.

Comparison Theorem for General Volterra-Stieltjes Integro-differential Equations

In this paper, A. B, Mingarelli's result is generalized to General Volterra-Stieltjes Integro-differential Equations. Comparison theorem and equivalence condition of non-oscillation are obtained.Clasical Sturm comparison theorem and some conclusions are generalized.

Regularization and Choice of the Parameter for the Third Kind Nonlinear Volterra-Stieltjes Integral Equation Solutions

The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.

Volterra－Stieltjes积分微分方程的振动性与谱分析

本文主要研究Ｖｏｌｔｅｒｒａ－Ｓｔｉｅｌｔｊｅｓ积分微分方程的振动性与谱性质，所用的方法主要是直接方法。文中得到几个振动性准则和离散谱准则，并将这些结果应用到常微分方程。