Ten owners of real estate in such district, or the owners of not less than ten percent in amount of the outstanding drainage bonds of such drainage district, may institute proceedings in the district court of the county issuing such bonds wherein the drainage district is located, by filing a petition which shall set forth the names and addresses of the ten petitioning real estate owners or the names and addresses of the petitioning owners of ten percent in amount of the drainage bonds of said district, that said bonds are in default as defined in section 468.570, that the petitioners have good reason to believe that said default cannot, or will not, be removed by payment under the present schedule of said district, and asking that the matters herein presented be reviewed by the court, and determined as provided by this part.