The determination of eigenvalues and eigenfunctions of a linear integral operator with a symmetrical kernel by means of group elimination of unknowns

1963 ◽  
Vol 2 (3) ◽  
pp. 419-432
Author(s):  
V.S. Shishov
Keyword(s):  
Integral Operator ◽  
Eigenvalues And Eigenfunctions ◽  
Linear Integral

On the p-norm of an Integral Operator in the Half Plane

2013 ◽  
Vol 56 (3) ◽  
pp. 593-601 ◽  
Author(s):  
Congwen Liu ◽  
Lifang Zhou
Keyword(s):  
Integral Operator ◽  
Half Plane ◽  
Integral Operators ◽  
Bergman Projection ◽  
Partial Answer ◽  
Upper Half Plane ◽  
Weighted Bergman Projection

Abstract.We give a partial answer to a conjecture of Dostanić on the determination of the norm of a class of integral operators induced by the weighted Bergman projection in the upper half plane.

scholarly journals Solvability ofNth Order Linear Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
P. Almenar ◽  
L. Jódar
Keyword(s):  
Integral Operator ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Boundary ◽  
Order Linear ◽  
Linear Integral ◽  
Necessary And Sufficient

This paper presents a method that provides necessary and sufficient conditions for the existence of solutions ofnth order linear boundary value problems. The method is based on the recursive application of a linear integral operator to some functions and the comparison of the result with these same functions. The recursive comparison yields sequences of bounds of extremes that converge to the exact values of the extremes of the BVP for which a solution exists.

scholarly journals Multiplicity of Periodic Solutions for Third-Order Nonlinear Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Xuxin Yang ◽  
Weibing Wang ◽  
Dingyang Lv
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Operator ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Integrodifferential Equation ◽  
Nonlinear Differential Equations ◽  
Third Order ◽  
Existence Of Periodic Solutions ◽  
Linear Integral

We study the existence of periodic solutions for third-order nonlinear differential equations. The method of proof relies on Schauder’s fixed point theorem applied in a novel way, where the original equation is transformed into second-order integrodifferential equation through a linear integral operator. Finally, examples are presented to illustrate applications of the main results.

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