<< if two people are in love, but they fight alot about little things, then is it possible for the relationship to work out?? >>
Sure, its possible. But, you both have to sit down and agree on a couple things.
First, you have to both agree that the relationship is worth it. Second, you both must agree that you're contributing to this problem. This doesn't mean blaming the other, saying things like "Well I wouldn't act like I do if you wouldn't act like you do. You provoke me." It means admitting that each of you is contributing something to this problem.
Third, you must explore underlying problems that are causing this friction between you. The problem isn't just that you fight about silly things, there is some underlying friction, resentment, or unhappiness that is causing you to use these silly things as a means to some end. What that might be, only you two can say; unresolved fights, unresolved guilt, unresolved resentment, basic dissatisfaction with where the relationship is going, etc. It might even be stress or some other unrelated problem that you take out on each other.
There are times when you have to agree to disagree for the sake of civility without holding a grudge against the other or using some future disagreement to settle things that were unresolved in earlier disagreements. That happens in relationship that seem to be spiraling into a lot of trivial fights and squabbles.
My parents do this. They fight over the salt or some totally f-cking stupid thing like that, but they're really not fighting about the salt. They're fighting about something that happened two years ago, but they've whipped that horse to death without coming to some sort of resolution they both can live with. So, they use the salt, or whatever, to keep this thing alive because one or both of them are not content with the outcome of whatever they're really angry about (that happened two or three or ten years ago).
Someone has to stand-up and be the adult in the relationship even when the emotional urge is to fight like children. Someone has to resist that emotional urge to be indignant or angry, and ask 'Do you realize we're fighting about the salt? Is salt really that big of a f-cking deal? What is this really about and what can we do to put it to rest?' Work on it, one day at a time, and if after a while things still don't seem to be going in the right direction, then someone is going to have to make a decision.
I used to be in a relationship with a girl I loved, and I believe she loved me, but we came to a similar point in our relationship. I wanted to analyze everything, the 'reason' we weren't getting along, I believed there was a logical and palpable 'reason' why our relationship had taken a bad turn. I believed if I could discover and understand this 'reason' then I could 'fix' things.
That is perfectly admirable up to a point, but I was still convinced I could find this 'reason' even though we had really exhausted all of our options. I didn't want to let go, I guess because I didn't want to admit failure, that I had failed to 'fix' this problem between us. I have a tendency to get rather tenacious about solving problems that matter to me. I begin to view it as a personal challenge to which I am very reluctant of admitting defeat.
But that can drive you insane in relationships, because the fact is sometimes there are no 'good' reasons why two formerly loving people begin to drift apart. Well, there IS a reason for everything, but not only is our ability to discern and discover that reason limited, but so is our ability to do something about it. There is a reason why people get Alzheimer's and we've been trying to find that reason for 30+ years. Even when we discover the cause of Alzheimer's, it may take another 30 years to do something about it (find an effective therapy or cure).
With love, at some point you have to cut your losses and move on. Love is like the stock market in many ways. Life is like the stock market, really. Making money (success) in the stock market isn't about possibilities, its about probabilities, likelihoods, and odds.
You don't throw money at a company which has a 'possibility' of making money, you throw money at a company that you believe is LIKELY to make money. If a stock is losing money, you don't decide to hold-on to that stock unless you believe it is LIKELY to turn around. People lose in the stock market (and in life) because they fail to recognize the difference between possibility and probability. If you stay in too long, based on some remote possibility that things will turn-around, the vast majority of people are going to lose...and lose big.
In retrospect, I held-on to that failing 'stock' far too long, clinging to some remote possibility, not a probability, that the relationship would turn-around. But, as they say, you will let go when you are ready to let go, and not a minute before, and I wasn't ready to let go until I was ready.
I blame nobody for the relationship failing, it is one of those situations where it serves absolutely no useful or beneficial purpose to assign 'blame', and ultimately, if you find yourself in a similar situation, I hope you will resist the urge to blame someone, too. Just learn from it and let it go.