The coincidence degree of some functional differential operators in spaces of periodic functions and related continuation theorems

1991 ◽  
pp. 76-87 ◽  
Author(s):  
Anna Capietto ◽  
Jean Mawhin ◽  
Fabio Zanolin
Keyword(s):  
Differential Operators ◽  
Coincidence Degree ◽  
Periodic Functions ◽  
Functional Differential

Discrete differential operators for periodic and two-periodic time functions

2019 ◽  
Vol 38 (1) ◽  
pp. 325-347 ◽  
Author(s):  
Tadeusz Sobczyk ◽  
Michał Radzik ◽  
Natalia Radwan-Pragłowska
Keyword(s):  
Differential Operators ◽  
High Accuracy ◽  
Large Set ◽  
Periodic Functions ◽  
Content Type ◽  
Second Derivatives ◽  
Non Linear ◽  
Discrete Operators ◽  
Linear Differential ◽  
Very High

Purpose To identify the properties of novel discrete differential operators of the first- and the second-order for periodic and two-periodic time functions. Design/methodology/approach The development of relations between the values of first and second derivatives of periodic and two-periodic functions, as well as the values of the functions themselves for a set of time instants. Numerical tests of discrete operators for selected periodic and two-periodic functions. Findings Novel discrete differential operators for periodic and two-periodic time functions determining their first and the second derivatives at very high accuracy basing on relatively low number of points per highest harmonic. Research limitations/implications Reduce the complexity of creation difference equations for ordinary non-linear differential equations used to find periodic or two-periodic solutions, when they exist. Practical implications Application to steady-state analysis of non-linear dynamic systems for solutions predicted as periodic or two-periodic in time. Originality/value Identify novel discrete differential operators for periodic and two-periodic time functions engaging a large set of time instants that determine the first and second derivatives with very high accuracy.

Solvability of first order functional differential operators

2015 ◽  
Vol 53 (9) ◽  
pp. 2065-2077
Author(s):  
Z. I. Ismailov ◽  
B. O. Guler ◽  
P. Ipek
Keyword(s):  
Differential Operators ◽  
First Order ◽  
Functional Differential

scholarly journals New Oscillation Criteria for Second-Order Forced Quasilinear Functional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Mervan Pašić
Keyword(s):  
Differential Equations ◽  
Differential Operators ◽  
Functional Differential Equations ◽  
Second Order ◽  
Laplacian Operator ◽  
Oscillation Criteria ◽  
Mixed Nonlinearities ◽  
Interval Oscillation ◽  
Functional Differential ◽  
The One

We establish some new interval oscillation criteria for a general class of second-order forced quasilinear functional differential equations withϕ-Laplacian operator and mixed nonlinearities. It especially includes the linear, the one-dimensionalp-Laplacian, and the prescribed mean curvature quasilinear differential operators. It continues some recently published results on the oscillations of the second-order functional differential equations including functional arguments of delay, advanced, or delay-advanced types. The nonlinear terms are of superlinear or supersublinear (mixed) types. Consequences and examples are shown to illustrate the novelty and simplicity of our oscillation criteria.

scholarly journals II. On the interchange of the variables in certain linear differential operators

1890 ◽  
Vol 181 ◽  
pp. 19-51
Keyword(s):  
Differential Operators ◽  
The Self ◽  
Differential Invariants ◽  
Linear Differential Operators ◽  
Independent Variable ◽  
The Subject ◽  
Functional Differential ◽  
Linear Differential ◽  
Derivatives Of ◽  
Single Relation

The operators to be considered, include or involve all those which have presented themselves as annihilators and generators in recent theories of functional differential invariants, reciprocants, cyclicants, &c. The general form of the binary operators, operators whose arguments are the derivatives of one dependent with regard to one independent variable, which I propose first to consider, is adopted in accordance with that used in two remarkable papers by Major MacMahon. They are his operators in four elements. The analogous ternary operators to which I subsequently devote attention, are distinct from his operators of six elements. Their arguments are the partial derivatives of one of three variables, supposed connected by a single relation, with regard to the two others. The only'previous contribution, of which I am aware, to the subject of the reversion of MacMahon operators, is a paper by Professor L. J. Rogers, in which he obtains the operator reciprocal to { μ, v ; 1, 1}, and alludes to the self reciprocal property of V which is expressed with more precision in (38) below.

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