Blow-Up of Solution to Cauchy Problem for the Singularly Perturbed Sixth-Order Boussinesq-Type Equation

We consider the singularly perturbed sixth-order Boussinesq-type equation, which describes the bidirectional propagation of small amplitude and long capillary gravity waves on the surface of shallow water for bond number (surface tension parameter) less than but very close to 1/3. The sufficient conditions of blow-up of solution to the Cauchy problem for this equation are given.

六阶边值问题的上下解方法

对六阶边值问题u(6)(x)= (x,u(x),u"(x),u(4)(x)),0<x<1,u(0)=u(1)=u"(0)=u"(1)=u(4)(0)=u(4)(1)=0,其中 :[0,1]×R3→R是连续的,赋予 一些条件,在边值问题上下解α,β存在的情况下,通过构造2个单调序列{αn}(非增),{βn}(非减),得到了该六阶边值问题在下解β和上解α之间解的存在性定理。文中无需要求 满足增长条件,从而发展了上下解的单调方法。最后通过实例给出其应用。

再生核空间W2^7[0,1]中求解六阶边值问题的新算法

本文研究了六阶边值问题的数值求解方法.利用再生核空间数值分析理论,获得了这类方程解的级数形式的精确表达式.

六阶边值问题的多个正解

在边值条件y(0)=y(1)=y″(0)=y″(1)=y(4)(0)=y(4)(1)=0或y(0)=y′(1)=y″(0)=y (1)=y(4)(0)=y(5)(1)=0下,研究方程d6y/dx6+h(x)f(y(x))=0的多个正解的存在性,在假定f满足在无穷远处超线性而在零点次线性的条件下获得至少有两个正解的结果.

非线性六阶周期边值问题正解的存在性与多重性

利用锥上的不动点定理和极大值原理,研究了六阶微分方程周期边值问题正解的存在性、多重性以及无穷可解性.引入控制函数,当非线性项f(x,y)的增长速度控制在适当的有界子集内时,得到了方程一个正解、n个正解和无穷多个正解的存在性.本文还讨论了正解的不存在性.

Finite Time Blow Up of Solution for 1-D Nonlinear Wave Equation of Sixth Order with Linear Restoring Force at High Energy Level

This paper is concerned with the Cauchy problem for some 1-D nonlinear wave equations of sixth order with linear restoring force. By utilizing the concavity method and the technique of anti-dissipativity a finite time blow up result of certain solutions with arbitrarily positive initial energy is presented.