Periodic Solution of Integro-Differential Equations Depended on Special Functions with Singular Kernels and Boundary Integral Conditions

2019 ◽  
pp. 1509-1520
Author(s):  
Raad Noori Butris ◽  
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Special Functions ◽  
Boundary Integral ◽  
Integral Conditions ◽  
Singular Kernels

scholarly journals Multiplicity of positive periodic solutions to second order differential equations

2006 ◽  
Vol 73 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O'Regan ◽  
R. P. Agarwal
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Second Order Differential Equations

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

scholarly journals Solving a System of Fractional-Order Volterra-Fredholm Integro-Differential Equations with Weakly Singular Kernels via the Second Chebyshev Wavelets Method

2021 ◽  
Vol 5 (3) ◽  
pp. 70
Author(s):  
Esmail Bargamadi ◽  
Leila Torkzadeh ◽  
Kazem Nouri ◽  
Amin Jajarmi
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Algebraic System ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Chebyshev Wavelets ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Kernels ◽  
Chebyshev Wavelet

In this paper, by means of the second Chebyshev wavelet and its operational matrix, we solve a system of fractional-order Volterra–Fredholm integro-differential equations with weakly singular kernels. We estimate the functions by using the wavelet basis and then obtain the approximate solutions from the algebraic system corresponding to the main system. Moreover, the implementation of our scheme is presented, and the error bounds of approximations are analyzed. Finally, we evaluate the efficiency of the method through a numerical example.

A Existence Theory for Positive Solutions to Superlinear Repulsive Singular Differential Equations with Impulse Effects

2010 ◽  
Vol 40-41 ◽  
pp. 149-155
Author(s):  
Zhang Xiao Ying ◽  
Guan Li Hong
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Singular Perturbation ◽  
Positive Solutions ◽  
Existence Theory ◽  
Singular Differential Equations ◽  
Perturbation Problem ◽  
Nonlinear Alternative

In this paper, we study positive solutions to the repulsive singular perturbation Hill equations with impulse effects. It is proved that such a perturbation problem has at least one positive impulsive periodic solution by a nonlinear alternative of Leray--Schauder.

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