SOLVABILITY OF A CLASS OF ELASTIC BEAM EQUATIONS WITH STRONG CARATHEODORY NONLINEARITY

Qingliu Yao

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SOLVABILITY OF A CLASS OF ELASTIC BEAM EQUATIONS WITH STRONG CARATHEODORY NONLINEARITY

机译：一类强阴极非线性弹性梁方程的可解性。

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摘要

We study the existence of a solution to the nonlinear fourth-order elastic beam equation with nonhomogeneous boundary conditions {u~(4)(t) = f(t,u(t),u'(t),u"(t),u'"(t)), a.e. t∈ [0,1], u(0) = a, u'(0) = 6, u(1) = c, u''(1) = d, where the nonlinear term f(t,u_0,u_1,u_2,u_3) is a strong Caratheodory function. By constructing suitable height functions of the nonlinear term f(t,u_0,u_1,u_2,u_3) on bounded sets and applying the Leray-Schauder fixed point theorem, we prove that the equation has a solution provided that the integration of some height function has an appropriate value.

机译：我们研究了具有非齐次边界条件{u〜（4）（t）= f（t，u（t），u'（t），u“（t）的非线性四阶弹性梁方程解的存在性，u'“（t）），ae t∈[0,1]，u（0）= a，u'（0）= 6，u（1）= c，u''（1）= d，其中非线性项f（t，u_0，u_1 ，u_2，u_3）具有很强的Caratheodory功能。通过在有界集合上构造非线性项f（t，u_0，u_1，u_2，u_3）的合适的高度函数并应用Leray-Schauder不动点定理，我们证明了该方程具有一个解决方案，只要对某些高度函数进行积分具有适当的值。

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来源
《Applications of Mathematics》 |2011年第6期|p.543-555|共13页
作者
Qingliu Yao;
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作者单位

Department of Applied Mathematics, Nanjing Uni-versity of Finance and Economics, Nanjing 210003, P. R. China;

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正文语种 eng
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关键词
nonlinear ordinary differential equation; boundary value problem; existence; fixed point theorem;

机译：非线性常微分方程边值问题;存在;不动点定理;

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专利

1. Solvability of a class of elastic beam equations with strong Carathéodory nonlinearity [J] . Yao Qingliu Applications of mathematics . 2011,第6期

机译：具有强Carathéodory非线性的一类弹性梁方程的可解性
2. Existence and non-existence of positive solutions of BVPs for fractional order elastic beam equations with a non-Caratheodory nonlinearity [J] . Yuji Liu Applied Mathematical Modelling . 2014,第2期

机译：具有非Caratheodory非线性分数阶弹性梁方程BVPs正解的存在性和不存在性
3. Existence of positive solutions of fractional-order elastic beam equation with a non-Caratheodory nonlinearity [J] . Liu Yuji Mathematical Methods in the Applied Sciences . 2016,第6期

机译：具有非卡拉特奥多非线性的分数阶弹性梁方程正解的存在性
4. Strong Solution of Initial-Boundary Value Problem for a Class of Nonlinear Thermoelastic Couple Beam Equations [C] . Cai-xian Wang, Jian-wen Zhang WISM 2011;International conference on web information systems and mining . 2011

机译：一类非线性热弹性耦合梁方程初边值问题的强解
5. Solving large sparse systems of nonlinear equations and nonlinear least squares problems using tensor methods on sequential and parallel computers*. [D] . Bouaricha, Ali. 1992

机译：在连续和并行计算机上使用张量法来求解非线性方程和非线性最小二乘问题的大型稀疏系统。
6. Contribution to Speeding-Up the Solving of Nonlinear Ordinary Differential Equations on Parallel/Multi-Core Platforms for Sensing Systems [O] . Vahid Tavakkoli, Kabeh Mohsenzadegan, Jean Chamberlain Chedjou, 2020

机译：用于加速对照对传感系统并行/多核平台的非线性常微分方程的贡献
7. Solvability of a class of elastic beam equations with strong Carathéodory nonlinearity [O] . Yao, Qingliu 2011

机译：具有强烈Carathéodory非线性的一类弹性梁方程的可解性
8. Positive Eigenfunctions for a Class of Second-Order Elliptic Equations with Strong Nonlinearity. [R] . clement, philippe 1976

机译：一类具有强非线性的二阶椭圆方程的正特征函数。

SOLVABILITY OF A CLASS OF ELASTIC BEAM EQUATIONS WITH STRONG CARATHEODORY NONLINEARITY

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