The Structure of a Positive Linear Integral Operator

1974 ◽  
Vol s2-8 (4) ◽  
pp. 711-718 ◽  
Author(s):  
Paul Nelson
Keyword(s):  
Integral Operator ◽  
Linear Integral

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.

scholarly journals On the Attracting Orbit of a Non-Linear Transformation Arising From Renormalization Of Hierarchically Interacting Diffusions Part I: The Compact Case

1995 ◽  
Vol 47 (1) ◽  
pp. 3-27 ◽  
Author(s):  
J. B. Baillon ◽  
PH. Clément ◽  
A. Greven ◽  
F. Den Hollander
Keyword(s):  
Integral Operator ◽  
Infinite System ◽  
Scaling Limit ◽  
Model Parameters ◽  
Interacting Diffusions ◽  
Time Scaling ◽  
Non Linear ◽  
Compact Case ◽  
Linear Integral ◽  
Class Of Functions

AbstractThis paper analyzes the n-fold composition of a certain non-linear integral operator acting on a class of functions on [0,1 ]. The attracting orbit is identified and various properties of convergence to this orbit are derived. The results imply that the space-time scaling limit of a certain infinite system of interacting diffusions has universal behavior independent of model parameters.

Global threshold dynamics of SIQS epidemic model in time fluctuating environment

2017 ◽  
Vol 10 (04) ◽  
pp. 1750060 ◽  
Author(s):  
Shang Li ◽  
Meng Fan ◽  
Xinmiao Rong
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Integral Operator ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Global Threshold ◽  
Linear Integral ◽  
Disease Free ◽  
The Basic Reproduction Number

The paper characterizes the global threshold dynamics of an epidemic model of SIQS type in environments with fluctuations, where the quarantine class is explicitly involved. Criteria are established for the permanence and extinction of the infective in environments with time oscillations. In particular, we further consider an environment which varies periodically in time. The global threshold dynamic scenarios i.e. the existence and global asymptotic stability of the disease-free periodic solution, the existence of the endemic periodic solution and the permanence of the infective are completely characterized by the basic reproduction number defined by the spectral radius of an associated linear integral operator.

Differential subordination results for Mittag-Leffler type functions with bounded turning property

2019 ◽  
Vol 69 (3) ◽  
pp. 573-582
Author(s):  
Hiba F. Al-Janaby ◽  
Maslina Darus
Keyword(s):  
Integral Operator ◽  
Differential Subordination ◽  
Regular Functions ◽  
Bounded Turning ◽  
Linear Integral

Abstract We aim to present a new linear integral operator and a certain subclass of regular functions with bounded turning property in correlation with the extended generalised Mittag-Leffler functions. Several results concerning an application of differential subordination are also investigated.

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