Positive solutions of singular Emden–Fowler boundary value problem with negative exponent and multiple impulses

In this paper, we first give the method of lower and upper solutions for the existence of positive solutions to a singular impulsive boundary value problem. Then we obtain a necessary and sufficient condition for the existence of positive solutions of Emden–Fowler singular impulsive boundary value problem by means of the method of lower and upper solutions.     

负指数的脉冲EMDEN-FOWLER方程奇异边值问题的正解

利用不动点定理得到了脉冲奇异混合边值问题的上下解方法,并且利用此方法得到了负指数的脉冲Emden-Fowler方程奇异混合边值问题正解存在的充分必要条件.     

负指数的脉冲EMDEN—FOWLER方程奇异边值问题的正解

利用不动点定理得到了脉冲奇异混合边值问题的上下解方法，并且利用此方法得到了负指数的脉冲Emden—Fowler方程奇异混合边值问题正解存在的充分必要条件．     

含有p-Laplacian算子的四阶奇异边值问题正解的存在性

研究了含p-Laplacian算子的奇异四阶四点边值问题,利用上下解方法与Schauder不动点定理,获得了至少一个C~3[0,1]正解的存在性结果.     

UPPER AND LOWER SOLUTIONS TO A NONLINEAR SEPARATED BOUNDARY VALUE PROBLEM

This paper is concerned with a third-order nonlinear separated boundary value problem. By the Leray-Schauder degree theory and the method of upper and lower solutions, we obtain the existence of at least three solutions to the problem.     

三阶奇摄动非线性边值问题

利用微分不等式理论，研究了某一类三阶奇摄动非线性边值问题。以二阶边值问题的已知结果为基础，引入Volterra型积分算子，建立了三阶非线性边值问题的上下解方法。在适当条件下，构造出具体的上下解，得出解的存在性和渐进估计。结果表明这种技巧也为三阶奇摄动边值问题的研究提出了崭新的思路。最后举例验证文中定理的正确性。     

POSITIVE SOLUTIONS TO FOURTH ORDER MULTI-POINT BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN OPERATOR

In this paper, we consider the existence of positive solutions to a singular fourth order p-Laplacian equation. By the upper and lower solution method and fixed point theorems, the existence of positive solutions to the boundary value problem is obtained under the assumption that the nonlinear term is decreasing.     

边界条件含参数的二阶奇异非线性边值问题

利用不动点指数理论以及上下解方法得到了边界条件含参数的二阶奇异非线性边值问题的正解存在性结果，该结果推广了已有文献中的众多结果．     

一阶时滞差分方程周期边值问题的单调迭代法

该文利用上下解结合单调迭代方法研究了一阶时滞差分方程周期边值问题解的存在性，假设问题的上下解存在，得到两组保证边值问题的极大极小解存在的充分条件.     

A Black-Scholes option pricing model with transaction costs

We consider a boundary value problem for a nonlinear differential equation which arises in an option pricing model with transaction costs. We apply the method of upper and lower solutions in order to obtain solutions for the stationary problem. Moreover, we give conditions for the existence of solutions of the general evolution equation.     

On a class of singular boundary value problems with singular perturbation

In this paper we investigate a class of singular second order differential equations with singular perturbation subject to three-point boundary value conditions, whose solution exhibits a couple of boundary layers at two endpoints. We first establish a lower–upper solutions theorem by using the Schauder fixed point theorem. By the asymptotic expansions and the lower–upper solutions theorem we obtain the existence, asymptotic estimates and uniqueness for the proposed problem. Several examples are given for illustrating our results.     

非线性三阶常微分方程的非线性三点边值问题解的存在性

基于上下解方法,在一定条件下,得到了一类带有非线性混合边界条件的三阶常微分方程的非线性三点边值问题解的存在性,作为上述存在性结果的应用,在推论中给出了一类三阶非线性微分方程三点边值问题解的存在性.     

Existence of solutions for anti-periodic boundary value problems

By using Schauder’s fixed point theorem and the lower and upper solutions method, we discuss the anti-periodic boundary value problem for a class of second-order differential equations. Some sufficient conditions for the existence of solutions are obtained.     

Generalized quasilinearization method for reaction-diffusion equations under nonlinear and nonlocal flux conditions

In this paper we consider an initial boundary value problem for a reaction-diffusion equation under nonlinear and nonlocal Robin type boundary condition. Assuming the existence of an ordered pair of upper and lower solutions we establish a generalized quasilinearization method for the problem under consideration whose characteristic feature consists in the construction of monotone sequences converging to the unique solution within the interval of upper and lower solutions, and whose convergence rate is quadratic. Thus this method provides an efficient iteration technique that produces not only improved approximations due to the monotonicity of its iterates, but yields also a measure of the convergence rate.     

Impulsive boundary value problems with nonlinear boundary conditions

In this paper, the upper and lower solution method and Schauder’s fixed point theorem are employed in the study of boundary value problems for a class of second-order impulsive ordinary differential equations with nonlinear boundary conditions. We prove the existence of solutions to the problem under the assumption that there exist lower and upper solutions associated with the problem.     

二阶脉冲泛函微分方程非线性边值问题

通过上下解和单调迭代技术讨论了二阶脉冲泛函微分方程非线性边值问题极值解的存在性,推广了相关文献的结果.     

Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth

The existence of stationary radial solutions to a partial differential equation arising in the theory of epitaxial growth is studied. It turns out that the existence or not of such solutions depends on the size of a parameter that plays the role of the velocity at which mass is introduced into the system. For small values of this parameter, we prove the existence of solutions to this boundary value problem. For large values of the same parameter, we prove the nonexistence of solutions. We also provide rigorous bounds for the values of this parameter, which separate existence from nonexistence. The proofs come as a combination of several differential inequalities and the method of upper and lower functions applied to an associated two‐point boundary value problem. Copyright © 2013 John Wiley & Sons, Ltd.     

ANTI-PERIODIC BOUNDARY VALUE PROBLEM FOR FUNCTIONAL DIFFENERTIAL EQUATION

By using upper and lower solutions coupled with monotone iterative technique, we discuss the anti-periodic boundary value problem for first order functional diffenertial equation. A sufficient condition for the existence of the solution is obtained.     

二阶微分方程反周期边值问题解的存在性

在这篇文章中,我们考虑了一类非线性二阶常微分方程反周期边值问题．利用上下解方法结合单调迭代技巧,我们得到了解的存在性结果．     

一类时滞反应扩散方程的周期解和概周期解

通过构造上、下控制函数，结合上、下解方法及相应的单调迭代方法研究了一类时滞反应扩散方程，证明了在反应项非单调时，如果一雏边值问题存在一对周期（或概周期）上、下解，则方程一定存在唯一的周期（或概周期）解．并给出了二维边值问题周期（或概周期）解存在唯一性的充分条件．推广了已有的一些结果。