scholarly journals An introduction to de Branges spaces of entire functions with applications to differential equations of the Sturm-Liouville type

1970 ◽  
Vol 5 (3) ◽  
pp. 395-471 ◽  
Author(s):  
Harry Dym
Keyword(s):  
Differential Equations ◽  
Entire Functions ◽  
Liouville Type ◽  
De Branges Spaces ◽  
Sturm Liouville

A high-speed method for eigenvalue problems. IV. Sturm-Liouville-type differential equations

1996 ◽  
Vol 96 (2-3) ◽  
pp. 247-262 ◽  
Author(s):  
T. Yano ◽  
K. Kitani ◽  
H. Miyatake ◽  
M. Otsuka ◽  
S. Tomiyoshi ◽  
...  
Keyword(s):  
Differential Equations ◽  
High Speed ◽  
Eigenvalue Problems ◽  
Liouville Type ◽  
Sturm Liouville ◽  
Speed Method

A Recursion Formula for the Coefficients of Entire Functions Satisfying an ODE with Polynomial Coefficients

2004 ◽  
Vol 11 (3) ◽  
pp. 409-414
Author(s):  
C. Belingeri
Keyword(s):  
Differential Equations ◽  
Sum Rules ◽  
Entire Functions ◽  
Recursion Formula ◽  
Linear Differential Equations ◽  
Bell Polynomials ◽  
Polynomial Coefficients ◽  
Linear Differential

Abstract A recursion formula for the coefficients of entire functions which are solutions of linear differential equations with polynomial coefficients is derived. Some explicit examples are developed. The Newton sum rules for the powers of zeros of a class of entire functions are constructed in terms of Bell polynomials.

scholarly journals On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1205
Author(s):  
Usman Riaz ◽  
Akbar Zada ◽  
Zeeshan Ali ◽  
Ioan-Lucian Popa ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Coupled System ◽  
Initial Boundary ◽  
Liouville Type ◽  
Liouville Derivative ◽  
Banach Contraction ◽  
Generalized Boundary Conditions

We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions.

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