I believe that this is a mistake and it should be "egne æble". I'm attending a danish course in Denmark and in my book is an information that after: den/det/de, min/mit/mine, din/dit/dine, sin/sit/sine, hans, hendes, vores, jeres, deres one should use e-form, for example: den store mand, min gode ven.
I also always write "egne". Even Wikipedia says "e-form or plural / definite, used in the plural and with a definite article, a pronoun or a genitive. den billige bog, "the cheap book"; hans store hus, "his big house" billige bøger, "cheap books"; store huse, "big houses""
so I don't know :/ I better not ask my boyfriend, he's ❤❤❤❤ with grammar xD
edit: okay, I think eget is right, even though I don't get why.