共查询到19条相似文献,搜索用时 109 毫秒
1.
2.
应用凸锥上的一个不动点定理,讨论了一类一维p-拉普拉斯四点边值问题在非线性项f依赖于未知函数的一阶导数的情况下拟对称正解的多重性,得到了这类边值问题存在多个拟对称正解的充分条件. 相似文献
3.
4.
在四阶微分方程非线性项f中含有未知函数“的二阶导数u”的情况下,运用Avery-Peterson不动点定理,研究了一类四阶微分方程三点边值问题三个正解的存在性,得到了该类边值问题存在三个正解的充分条件. 相似文献
5.
改进了奇异非线性边值问题的经典Agarwal-O'Regan方法.利用这个改进的方法建立了奇异非线性(p,n-p)共轭边值问题正解的局部存在性与多解性,其中允许非线性项关于时间和空间变元同时奇异.主要工具是锥拉伸与锥压缩型的Guo-Krasnosel'skii不动点定理和精确先验估计技巧.特别的,考察了非自治奇异非线性二阶、三阶、四阶共轭边值问题. 相似文献
6.
研究了一类非线性四阶微分方程奇异Sturm-Liouville边值问题,利用锥上的不动点定理得到了这类方程的C~3[0,1]正解和C~2[0,1]正解存在的充分必要条件. 相似文献
7.
8.
本文研究了一类非线性项带导数的p-Laplacian算子的分数阶微分方程边值问题正解的存在性和多解性.首先,利用分数阶微分方程和边值条件给出了该边值问题的Green函数,然后利用Guo-Krasnosel’skii’s不动点定理和Leggett-Williams不动点定理得出该边值问题一个或者三个正解的存在性结论.作为应用,给出两个例子验证了结论的适用性,特别是,用迭代法进行了逼近模拟,给出解的图形.值得一提的是此文研究的微分方程的非线性项是带有Riemann-Liouville型分数阶微分. 相似文献
9.
本文利用上、下解方法讨论了几类n阶常微分方程三、四点非线性边值问题解的存在性和唯一性。 相似文献
10.
11.
On fourth-order elliptic boundary value problems 总被引:4,自引:0,他引:4
C. V. Pao 《Proceedings of the American Mathematical Society》2000,128(4):1023-1030
This paper is concerned with the existence and uniqueness of a solution for a class of fourth-order elliptic boundary value problems. The existence of a solution is proven by the method of upper and lower solutions without any monotone nondecreasing or nonincreasing property of the nonlinear function. Sufficient conditions for the uniqueness of a solution and some techniques for the construction of upper and lower solutions are given. All the existence and uniqueness results are directly applicable to fourth-order two-point boundary value problems.
12.
考察了一类含有所有导数的半线性四阶两点边值问题的解和正解的存在性.在力学中,这类边值问题描述了一端简单支撑,另一端被滑动夹子夹住的弹性梁的形变.结论表明,只要非线性项在其定义域的某个有界集上的“最大高度”是适当的,那么这类问题至少存在一个解或者正解. 相似文献
13.
Yuan-Ming Wang 《Applied Numerical Mathematics》2011,61(1):38-52
The purpose of this paper is to give a numerical treatment for a class of strongly nonlinear two-point boundary value problems. The problems are discretized by fourth-order Numerov's method, and a linear monotone iterative algorithm is presented to compute the solutions of the resulting discrete problems. All processes avoid constructing explicitly an inverse function as is often needed in the known treatments. Consequently, the full potential of Numerov's method for strongly nonlinear two-point boundary value problems is realized. Some applications and numerical results are given to demonstrate the high efficiency of the approach. 相似文献
14.
Xiaoqing Deng 《Journal of Applied Mathematics and Computing》2014,45(1-2):1-14
In this paper, a class of fourth-order nonlinear difference equations are considered. By making use of the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for mixed boundary value problems and give some new results. Our results successfully complement the existing results in the literature. 相似文献
15.
四阶非线性常微分方程非线性两点边值问题解的存在唯一性 总被引:2,自引:0,他引:2
裴明鹤 《高校应用数学学报(A辑)》1995,(3):285-294
本文利用Bolzano定理,给出了四阶非线性常微微分方程具有非线性边界条件的两点边值问题(1)(2)2,(1)(2)3存在解与存在唯一解的一般性结果,并将所得结果应用于Lipschiz方程,对Lipschitz方程满足边界条件(2)2,(2)3的边值问题给出了存在解与存在唯一解的具体的充分条件。 相似文献
16.
In this paper, we establish an existence criterion of triple positive solutions of a class of nonlinear fourth-order three-point boundary value problem by the LeggettWilliams fixed point theorem. The interesting point is that the nonlinear term is involved with all low-level derivatives. 相似文献
17.
Qingliu Yao 《Applicable analysis》2013,92(1):97-107
The existence of m positive solutions is proven for a nonlinear fourth-order boundary value problem with two parameters, where m is an arbitrary natural number. This kind of fourth-order boundary value problems usually describes the equilibrium state of elastic beam where both ends are simply supported. The main ingredient is Krasnosel'skii fixed point theorem of cone expansion–compression type. 相似文献
18.
Fazhan Geng 《Applied mathematics and computation》2009,213(1):163-169
This paper presents a new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems. It is a relatively new analytical technique. The solution obtained by using the method takes the form of a convergent series with easily computable components. This paper will present a numerical comparison between our method and other methods for solving an open fourth-order boundary value problem presented by Scott and Watts. The method is also applied to a nonlinear fourth-order boundary value problem. The numerical results demonstrate that the new method is quite accurate and efficient for fourth-order boundary value problems. 相似文献
19.
利用一个已有的抽象结论,证明了一类非线性四阶方程两点边值问题变号解的存在性. 相似文献