Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Abdourahman Haman Adji and Shankishvili Lamara Dmitrievna
Pages: [53] - [69]
Received Date: September 18, 2024
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122311
The main objective set in this research work is to carry out
investigations on the study of the existence of solutions (solutions
centered on zero), in the distributional sense, of the non-homogeneous
Euler linear singular differential equation of order l of the
general following form 
where l is a natural number not equal to
zero; 
are two natural numbers, 
real numbers and more 
is the Dirac distributional centered on 0 and
is the s-th-order derivative of the
Dirac delta distribution.
In the scientific work undertaken in some of our published articles,
we have completely carried out the investigations on the study of the
solvency of the singular linear differential equation of the first
order. Confer our references. This allowed us to obtain the conditions
of solvency of the equation in question and, we were able to
exhaustively identify all the solutions, both distributional and
classical, according to the different relationships between the
parameters appearing in the latter. Even further in depth, we carried
out investigations relating to the same type of equation in 
a distributional space larger than 
to realize the existence of other solutions of
another nature to the homogeneous equation associated with the
non-homogeneous equation. All this leads us to imagine, from then on,
the situation which could arise from the same questions of
investigation in relation to a general singular equation of order
l. We make an exhaustive description of all distributional
solutions centered on zero of this equation in the functional space of
distributions 
test functions, generalized functions, distributions, Dirac delta function, zero-centered solutions.
