On a class of linear integro-differential equations

Author(s):  
H. R. Pitt

This paper is a sequel to a previous one(1) with the same title which dealt with the general solution of equations of the typeWe consider here the more general equationwhere g(x) is a given function. We are interested particularly in the existence and uniqueness of solutions of the latter equation and show how these are related to the closure and completeness properties of sets of functions {xneωnx} derived from the kernels kr(y).

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Jianjie Wang ◽  
Ali Mai ◽  
Hong Wang

Abstract This paper is mainly devoted to the study of one kind of nonlinear Schrödinger differential equations. Under the integrable boundary value condition, the existence and uniqueness of the solutions of this equation are discussed by using new Riesz representations of linear maps and the Schrödinger fixed point theorem.


2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Xia Wang ◽  
Run Xu

In this paper, we research CFR fractional differential equations with the derivative of order 3<α<4. We prove existence and uniqueness theorems for CFR-type initial value problem. By Green’s function and its corresponding maximum value, we obtain the Lyapunov-type inequality of corresponding equations. As for application, we study the eigenvalue problem in the sense of CFR.


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