A special assessment shall be made only upon petition signed and sworn to by one (1) or more persons owning land within the proposed district, and praying that provision be made for funds to defray the preliminary costs and expenses already incurred up to that stage of the proceedings. Upon the filing of such petition, the court shall set a day for the hearing of that matter and direct that publication for all landowners within the proposed district who are not petitioners in the petition be made in some newspaper published in the county in which the district is located, and if located in more than one (1) county, then in a publication in each county in which the land in the proposed district is located, the publication to be made for three (3) consecutive weeks, the last publication to be at least ten (10) days before the day set for the hearing. The publication shall notify such landowners of the pending suit and the prayer of the petition for the creation and collection of a fund to pay the preliminary costs and expenses and the day fixed for the hearing, and notify the landowners not petitioners in the petition to appear and show cause why an assessment to create the fund should not be made. The landowners shall make their appearance and file their objections, if any, on or before twelve o'clock (12:00) noon of the day set for hearing.