Periodic solution generated by impulses for singular differential equations

Nonconstant 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...

Positive Periodic Solution for Second-Order Singular Semipositone Differential Equations

and Applied Analysis 3

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

The Legendre Wavelet Method for Solving Singular Integro-differential Equations

In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.

Existence and multiplicity of periodic solutions generated by impulses

and Applied Analysis 3 Remark 1.3. It is easy to see that V ′ 1 , V ′ 2 are weaker than V1 , V2 . Therefore, Theorem 1.2 improves Theorem A. Indeed, taking V t, u −|u| − |u|, 1 < γ < ς ≤ 2, Gk u −|u|, 1.3 all conditions in Theorem 1.4 are satisfied, but conditions in Theorem A cannot be satisfied. Theorem 1.4. Assume that V1 , V2 hold. Moreover, the following conditions are satisfied: V3 Vu t, ...