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ON THE INTEGRATING FACTOR OF ABEL EQUATION
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作者 应益荣 党新益 《Annals of Differential Equations》 1995年第1期114-116,共3页
The necessary and sufficient condition of a sort of rational faction integrating factor of Abel equation is derived from this paper.
关键词 abel equation integrating factor
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ON THE EQUIVALENCE OF THE ABEL EQUATION 被引量:3
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作者 Zhang Shanlin Zhou Zhengxin (Dept. of Math., Yangzhou University, Yangzhou 225002) 《Annals of Differential Equations》 2006年第3期461-466,共6页
This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these ... This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations. 展开更多
关键词 abel equation reflective function EQUIVALENCE periodic solution
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On the Center Problem for Generalized Abel Equations
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作者 Chang Jian LIU Shao Qing WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第12期2329-2337,共9页
This paper is devoted to the conditions of the existence of CC-center for the generalized Abel equations.Using some new original methods,we obtain extended results of the main theorems in the paper by Llibre and Valls... This paper is devoted to the conditions of the existence of CC-center for the generalized Abel equations.Using some new original methods,we obtain extended results of the main theorems in the paper by Llibre and Valls(2020)and the one by Zhou(2020),respectively.The proofs in this paper are much simpler than the previous ones. 展开更多
关键词 Generalized abel equation composition condition center problem
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GENERAL SOLUTION OF A 2-D WEAK SINGULAR INTEGRAL EQUATION WITH CONSTRAINT AND ITS APPLICATIONS
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作者 云天铨 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第8期749-755,共7页
In this paper, the solution, more general than [1], of a weak singular integral equation integral(0)(pi)integral(-infinity)(infinity) p(s,psi)d sk(psi)d psi=F(r,theta), (r,theta)epsilon (Q) over bar=Q+partial derivati... In this paper, the solution, more general than [1], of a weak singular integral equation integral(0)(pi)integral(-infinity)(infinity) p(s,psi)d sk(psi)d psi=F(r,theta), (r,theta)epsilon (Q) over bar=Q+partial derivative Q subject to constraint p(s,psi)=0, for (s,psi)=(r,theta)is not an element of Q={r,theta)/F(r,theta)>c*} is found p=2/pi[root w g'(0)+integral(0)(w) root w-u g '(u)du] where k and F are given continuous functions; (s,psi) is a local polar coordinating with origin at M(r,theta); (r,theta) is the global polar coordinating with origin at O(0,0) F(r,theta)=c* (const.) is the boundary contour partial derivative Q of the considered range Q; g(w)=F(r,theta)/[pi k(psi(0))]; g'=dg/dw; w=N-r(2)sin(2)(theta+psi(0)); psi(0) and N are mean values. The solution shown in type (2.19) of [1] is a special case of the above solution and only suits F(r,theta)=w. The solution of a rigid cone contact with elastic half space, more simple and clear than Love's (1939), is given as an example of application. 展开更多
关键词 radon transform abel integral equation theorem mean value Hertz's solution
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THE PROBLEM OF AN EXTERNAL CIRCULAR CRACK UNDER ASYMMETRIC LOADINGS
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作者 WANG Yin-bang(王银邦) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第1期10-16,共7页
Using the boundary integral equation method, the problem of an external circular crack in a three-dimensional infinite elastic body under asymmetric loadings is investigated. The two-dimensional singular boundary inte... Using the boundary integral equation method, the problem of an external circular crack in a three-dimensional infinite elastic body under asymmetric loadings is investigated. The two-dimensional singular boundary integral equations of the problem were reduced to a system of Abel integral equations by means of Fourier series and hypergeometric functions. The exact solutions of stress intensity factors ore obtained for the problem of an external circular crack under asymmetric loadings, which are even more universal than the results obtained by the use of Hankel transform method. The results demonstrate that the boundary integral equation method has great potential as a new analytic method. 展开更多
关键词 external circular crack asymmetric loadings boundary integral equations abel equations stress intensity factors exact solutions
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WORD PROBLEMS AND THE CENTERS OF ABEL DIFFERENTIAL EQUATIONS
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作者 M.A.M.Alwash(University of California, Los Angeles, CA 90024, USA) 《Annals of Differential Equations》 1995年第4期392-396,共5页
The approach of word problems is adopted to study the centers of nonautonomous cubic equations.We answer various questions that arise from this investigation. In particular.we demonstrate that a recent condition for t... The approach of word problems is adopted to study the centers of nonautonomous cubic equations.We answer various questions that arise from this investigation. In particular.we demonstrate that a recent condition for the existence of a center is not necessary. 展开更多
关键词 abel WORD PROBLEMS AND THE CENTERS OF abel DIFFERENTIAL equationS
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An Approximate Approach for Systems of Singular Volterra Integral Equations Based on Taylor Expansion
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作者 Mohsen Didgar Alireza Vahidi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2018年第8期145-152,共8页
In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of un... In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance. 展开更多
关键词 systems of singular Volterra integral equations (SSVIEs) systems of generalized abel's integral equations error analysis Taylor expansion
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ON THE DECISION PROBLEM OF THE CENTER OR FOCUS FOR A CLASS OF PLANAR POLYNOMIAL FIELDS
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作者 谢向东 蔡燧林 《Annals of Differential Equations》 1998年第1期81-90,共10页
In this paper we study the decision problem of the center or focus for a class of planar polynomial fields which can be changed into Abel equation. Taking a Poincaré return map h(x) , we can calculate any orde... In this paper we study the decision problem of the center or focus for a class of planar polynomial fields which can be changed into Abel equation. Taking a Poincaré return map h(x) , we can calculate any order derivative of h(x) at x=0 and obtain the focus value of each order. The new method in this paper avoids the recurence operation and reduces the work in calculating the focus value. 展开更多
关键词 decision problem of the center or focus abel equation Poincaré return map.
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Darboux integrability and algebraic limit cycles for a class of polynomial differential systems
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作者 CAO JinLong LLIBRE Jaume ZHANG Xiang 《Science China Mathematics》 SCIE 2014年第4期775-794,共20页
This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems x=x-y+P n+1(x,y)+xF2n(x,y),y=x+y+Q n+1(x,y)+yF2n(x,y),where P i(x,y),Q i(x,y)and F i(x,y)are homogeneous po... This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems x=x-y+P n+1(x,y)+xF2n(x,y),y=x+y+Q n+1(x,y)+yF2n(x,y),where P i(x,y),Q i(x,y)and F i(x,y)are homogeneous polynomials of degree i.Within this class,we identify some new Darboux integrable systems having either a focus or a center at the origin.For such Darboux integrable systems having degrees 5and 9 we give the explicit expressions of their algebraic limit cycles.For the systems having degrees 3,5,7 and 9and restricted to a certain subclass we present necessary and sufficient conditions for being Darboux integrable. 展开更多
关键词 Darboux first integral algebraic limit cycles abel differential equation
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