Results on the Well Posedness of a Distributional Differential Problem
Keywords:Distributional differential equation, zeros of a polynomial, existence of solution, periodic distributional space, Fourier inverse transform
In this work, we study the Fourier Theory in the space of periodic distributions: P’. We analyze the existence of at least one solution for the distributional differential problem in connection with the zeros of a polynomial. We prove that there are infinite solutions when the Fourier coefficients vanish at the integer zeros of the polynomial and otherwise does not have solution. We deduce the existence and uniqueness by considering that the polynomial lacks integer zeros. In the cases of existence, we deduce the analytical solutions. Moreover, we get a result firelated with the continuous dependence of the solution. Finally, we give some conclusions and applications.
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