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通过几个实例给出解非预解形式线性微分方程的一般方法,并讨论了预解形式的线性微分方程与非预解形式的线性微分方程解集的差别. 相似文献
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针对柱对称二维流体力学方程组,基于考虑方程右端附加源项的人为构造解方法,构造出一类统一形式的人为解.此类形式的人为解,对验证多维流体力学应用程序的正确性有重要的作用.同时将该类统一形式的人为解应用到PPM格式的程序,验证了构造的人为解的可行性. 相似文献
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在局部凸空间中引进了向量均衡问题的强超有效解、C-强超有效解、弱超有效解, C-弱超有效解、齐次超有效解、 C-齐次超有效解的概念,并在局部凸空间中用极理论为工具讨论了向量均衡问题的 C-弱超有效解, C-超有效解, C-齐次超有效解,以及C-强超有效解的对偶形式. 又在赋范线性空间中讨论了向量均衡问题的以上各种超有效解之间的等价性,并且在赋范线性空间具正规锥的条件下讨论了向量均衡问题的以上各种超有效解的对偶形式. 作为它的应用,给出了向量优化问题各种超有效解的对偶形式. 相似文献
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研究了一类非线性三阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用不动点原理证明了原问题解的存在性及所得形式渐近解的一致有效性. 相似文献
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通过Ibragimov新守恒定理的基本思想,构造了动力学Drinfel’d-Sokolov-Wilson(DSW)方程的局部守恒定律.并且利用Hirota双线性形式推导出该方程的双线性Backlund变换,在双线性Backlund变换的基础上,获得该方程的行波解.然后构造DSW方程的正四次函数、二次函数及指数函数所组合的形式解,另外构造了正四次函数、二次函数、三角函数和双曲函数组合的形式解,通过计算求解出DSW方程相应的高阶Lump解与Kink解、高阶Lump解与周期波解的相互作用解,同时验证了该方程解的存在性. 相似文献
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广义射影Riccati方程方法与(2+1)维色散长波方程新的精确行波解 总被引:2,自引:0,他引:2
助于符号计算软件Maple,通过一种构造非线性偏微分方程更一般形式行波解的直接方法,即改进的广义射影Ricccati方程方法, 求解(2+1)维色散长波方程,
得到该方程的新的更一般形式的行波解, 包括扭状孤波解, 钟状解,孤子解和周期解. 并对部分新形式孤波解画图示意. 相似文献
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该文在L2中讨论了第一类算子方程Au=f当A-1无定义和A-1不是单值的情形下的不适定求解问题,给出了解存在的充要条件,当有解时,得到了形式解,多解时形式解就是最小范数解,并且得到了近似解表达式,给出了误差估计. 相似文献
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本文研究一类奇摄动二阶脉冲微分方程非线性边值问题.在适当的假设下,利用合成展开法分段构造“脉冲层”和边界层的联立展开法构造所述问题的形式渐近解,借助上、下解方法证明原问题的解的存在性和形式解的一致有效性. 相似文献
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In this paper the authors consider the summability of formal solutions for some first order singular PDEs with irregular singularity. They prove that in this case the formal solutions will be divergent, but except a enumerable directions, the formal solutions are Borel summable. 相似文献
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G. K. Immink 《Journal of Difference Equations and Applications》2013,19(7):769-776
We prove a Maillet type theorem for formal solutions of nonlinear difference systems, relating the Gevrey order of the formal solutions to the lowest level of an associated, linear difference operator. 相似文献
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研究了一类含双参数的非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性. 相似文献
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Yasutaka Sibuya 《Journal of Differential Equations》2003,190(2):559-578
This paper is a continuation of the previous paper (J. Differential Equations 165 (2000) 255). The main subject is the Gevrey property of formal solutions of an analytic ordinary differential equation in powers of a parameter. In one case, a given formal solution itself is of the Gevrey type, while, in another case, the existence of a formal solution implies the existence of formal solutions of the Gevrey types. These situations are explained systematically in this paper. 相似文献
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在 Reid等人标准型概念的基础上 ,引进形式可积系统的概念 .并给出验证形式可积系统解的完备性的机械化算法 ,并用此方法证明了各向同性弹性力学方程组的胡海昌解的完备性问题 . 相似文献
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Agostino Prástaro 《Journal of Mathematical Analysis and Applications》2006,321(2):930-948
In the framework of the geometry of PDE's, we classify variational equations of any order with respect to their formal properties. Following our previous results [A. Prástaro, Quantized Partial Differential Equations, World Scientific, Singapore, 2004], we relate constrained variational PDE's to their integral bordism groups. In this way we are able to characterize global solutions of constrained variational PDE's and to relate them to the structure of global solutions for the corresponding constraint equations. Some applications are also considered. 相似文献
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《Journal of Differential Equations》2014,257(8):3048-3070
We study the k-summability of divergent formal solutions for the Cauchy problem of a certain class of linear partial differential operators with time dependent coefficients. The problem is reduced to a k-summability property of formal solutions for a linear similar ordinary differential equation associated with the Cauchy problem. 相似文献
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In this paper, some analytic approaches are formulated for the existence of analytic solutions of analytic nonlinear difference equations. From the point of view of dynamical systems, analytic solutions of such kinds of equations can be generally expressed by formal power series of exponential variables, so we are interested in considering a difference equation as a q-difference equation via a suitable coordinate transformation. After stating analytic results for formal series solutions of nonlinear q-difference equations, we also derive some results for the existence of analytic solutions to autonomous rational difference equations. 相似文献
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V.M Raman 《Journal of Mathematical Analysis and Applications》1983,94(2):536-560
A usable, not technically complicated theory unlike that of Wasow of linear, singular, even order differential operators with general boundary conditions is proposed and the behaviour of eigenvalues and eigenfunctions is discussed in the limit as ε → 0, ε > 0. Completeness of the eigenvalue spectrum when the operator is formally self-adjoint is discussed and formal solutions are constructed and finally justification of the formal approximations is shown by proving the existence of actual solutions of the differential equation approximated by formal solutions. Also, modifications necessary for the consideration of the critical point are suggested. This theory is unlike that of Reid since it provides rigorous justification of the approximations and moreover, this theory is applicable to a large class of physical problems rewritten in such a way that they contain a small parameter. 相似文献