You may have a problem establishing an adverse possession claim if your use of the are has not been exclusive - in other words, the fact that your neighbors are using the area, too, may hurt your case. You need to talk to a lawyer in your area who is familiar with adverse possession.
Adverse possession is a common law concept, and does not apply in Louisiana. The closest Louisiana concept is acquisitive prescription. Louisiana Civil Code Article 3476 provides:
"The possessor must have corporeal possession, or civil possession preceded by corporeal possession, to acquire a thing by prescription.
The possession must be continuous, uninterrupted, peaceable, public, and unequivocal."
For a person acting in good faith -- that is, the person thinks he actually is the owner of the land -- the period needed to acquire the land is 10 years; for a person not acting in good faith, the period is 30 years. From your description, it appears that your situation fails to meet the requirements for acquisitive prescription.