scholarly journals Coexistence of analytic and distributional solutions for linear differential equations, II

1991 ◽  
Vol 159 (1) ◽  
pp. 271-289 ◽  
Author(s):  
Joseph Wiener ◽  
Kenneth L Cooke ◽  
S.M Shah
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Distributional Solutions ◽  
Linear Differential

scholarly journals Finite Series of Distributional Solutions for Certain Linear Differential Equations

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 116
Author(s):  
Nipon Waiyaworn ◽  
Kamsing Nonlaopon ◽  
Somsak Orankitjaroen
Keyword(s):  
Differential Equations ◽  
Delta Function ◽  
Dirac Delta Function ◽  
Linear Differential Equations ◽  
Dirac Delta ◽  
Finite Series ◽  
Distributional Solutions ◽  
Linear Differential

In this paper, we present the distributional solutions of the modified spherical Bessel differential equations t2y″(t)+2ty′(t)−[t2+ν(ν+1)]y(t)=0 and the linear differential equations of the forms t2y″(t)+3ty′(t)−(t2+ν2−1)y(t)=0, where ν∈N∪{0} and t∈R. We find that the distributional solutions, in the form of a finite series of the Dirac delta function and its derivatives, depend on the values of ν. The results of several examples are also presented.

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