Derivation of the Fredholm Theory from a Differential Equation of Infinite Order

1926 ◽  
Vol 28 (1/4) ◽  
pp. 309
Author(s):  
H. T. Davis
Keyword(s):  
Differential Equation ◽  
Infinite Order ◽  
Fredholm Theory

scholarly journals On the Growth of Solutions of Some Second Order Linear Differential Equations with Entire Coefficients

2013 ◽  
Vol 21 (2) ◽  
pp. 35-52
Author(s):  
Benharrat Belaïdi ◽  
Habib Habib
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Infinite Order ◽  
Entire Functions ◽  
Complex Numbers ◽  
Order Of Growth ◽  
Hyper Order ◽  
Linear Differential ◽  
Growth Of Solutions

Abstract In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation where n≥2 is an integer, Aj (z) (≢0) (j = 1,2) are entire functions with max {σ A(j) : (j = 1,2} < 1, Q (z) = qmzm + ... + q1z + q0 is a nonoonstant polynomial and a1, a2 are complex numbers. Under some conditions, we prove that every solution f (z) ≢ 0 of the above equation is of infinite order and hyper-order 1.

scholarly journals On integral solutions of the differential equation of infinite order with polynomial coefficients

1964 ◽  
Vol 4 (2) ◽  
pp. 203-227
Author(s):  
J. F. Korobeinik
Keyword(s):  
Differential Equation ◽  
Infinite Order ◽  
Polynomial Coefficients ◽  
Integral Solutions

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Ю. Ф. Коробейник. О целых решениях дифференциального уравнения бесконечного порядка J. F. Korobeinik. Begalinės eilės diferencialinės lygties su polinominiais koeficientais sveikieji sprendiniai

scholarly journals Infinite growth of solutions of second order complex differential equation

2018 ◽  
Vol 16 (1) ◽  
pp. 1233-1242
Author(s):  
Guowei Zhang
Keyword(s):  
Differential Equation ◽  
Trivial Solution ◽  
Infinite Order ◽  
Order Differential Equation ◽  
Second Order ◽  
Order Complex ◽  
Complex Differential Equation ◽  
Second Order Differential Equation ◽  
Growth Of Solutions

AbstractIn this paper we study the growth of solutions of second order differential equation f′′ + A(z)f′ + B(z)f = 0. Under certain hypotheses, the non-trivial solution of this equation is of infinite order.

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