You have the same problem as me.

You have the same jacket as "him" or "me".

You have the same problem as "him" or "me".

It is a problem of mine. Let me handle it.

I need the support of Tom.

Please check.

tufguy said:

It is a problem of mine let me handle it.

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You have a run-on sentence there. Please use the "Edit Post" function to edit post #1. Please don't write another new post with an amended version.

With your edit, all the sentences are correct. A few very old-fashioned and, in my opinion, unrealistic grammarians will say that you (and practically everyone else) are using the wrong pronouns and should write as he or as I.​ Pay no attention; they're trying to make you do something extremely unnatural.

May I ask a question here?

How about "you have the same problem as mine"?

Is it OK, too?

tzfujimino said:

May I ask a question here?

How about "you have the same problem as mine"?

Is it OK, too?

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No. You can say Your problem is the same as mine, though.

GoesStation said:

No. You can say Your problem is the same as mine, though.

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I need support of 'you' or 'your's'?"

You didn't tell me that my (problem) sentence was wrong.

tufguy said:

I need support of 'you' or 'your's'?"

You didn't tell me that my (problem) sentence was wrong.

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I'd say I need support from you.

tzfujimino said:

I'd say I need support from you.

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If I am talking about a third person then I cannot use your version.

No, but you can change "you" to "Tom" to make it more like your original. Like your other recent thread, using the standard possessive (apostrophe + s) is more natural. If you're only looking for support from one person or from a single group, the possessive form is best, in my opinion.

I need Tom's support. (Correct and most natural.)
I need support from Tom. (Correct but less natural.)

I need my friends' support. (Correct and most natural.)
I need support from my friends. (Correct but less common.)

I need Tom's and my friends' support. (Grammatical but awkward.)
I need support from Tom and [from] my friends. (Much better.)

tufguy said:

I need support of 'you' or 'your's'?"

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We never write your's​.