Periodic Solutions with Nonconstant Sign in Abel Equations of the Second Kind
نویسنده
چکیده
The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation x 7→ x−1, and there are many results available in the literature for the first kind equation. However, the equivalence breaks down when one seeks for solutions with nonconstant sign. This note is devoted to periodic solutions with nonconstant sign in Abel equations of the second kind. Specifically, we obtain sufficient conditions to ensure the existence of a periodic solution that shares the zeros of the leading coefficient of the Abel equation. Uniqueness and stability features of such solutions are also studied.
منابع مشابه
Existence of Periodic Solutions with Nonconstant Sign in a Class of Generalized Abel Equations
This article provides sufficient conditions for the existence of periodic solutions with nonconstant sign in a family of polynomial, non-autonomous, first-order differential equations that arise as a generalization of the Abel equation of the second kind.
متن کاملA new uniqueness criterion for the number of periodic orbits of Abel equations
A solution of the Abel equation ẋ = A(t)x + B(t)x such that x(0) = x(1) is called a periodic orbit of the equation. Our main result proves that if there exist two real numbers a and b such that the function aA(t) + bB(t) is not identically zero, and does not change sign in [0, 1] then the Abel differential equation has at most one nonzero periodic orbit. Furthermore, when this periodic orbit ex...
متن کاملNonconstant periodic solutions created by impulses for singular differential equations
*Correspondence: [email protected] 2Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 5046, Dhahran, 31261, Saudi Arabia Full list of author information is available at the end of the article Abstract In this work we discuss the existence of nonconstant periodic solutions for nonautonomous singular second order differential equations in the p...
متن کاملThe Use of Fuzzy Variational Iteration Method For Solving Second-Order Fuzzy Abel-Volterra Integro-Differential Equations
In this paper, fuzzy variational iteration method (FVIM) is proposed to solve the second- order fuzzy Abel-Volterra integro-differential equations. The existence and uniqueness of the solution and convergence of the proposed method are proved in details. is investigated to verify convergence results and to illustrate the efficiently of the method.
متن کاملSolving Volterra Integral Equations of the Second Kind with Convolution Kernel
In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad et al., [K. Maleknejad and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, Appl. Math. Comput. (2005)] to gain...
متن کامل