Pseudodifferential Equations with Regular Singularity for Radial Functions of the p-Adic Argument

We consider the case of regular singularity for a class of equations with pseudodifferential operator D^α, α > 0, on radial functions \({\left|t\right|}_{p}^{\alpha }\left({D}^{\alpha }\right)\left({\left|t\right|}_{p}\right)=A\left({\left|t\right|}_{p}\right)u\left({\left|t\right|}_{p}\right).\) $${\left|t\right|}_p^{\alpha }\left(D^{\alpha }\right)\left({\left|t\right|}_p\right)=A\left({\left|t\right|}_p\right)u\left({\left|t\right|}_p\right).$$

Under certain conditions, we prove the existence of a solution specified in the form of a locally absolutely convergent power series.