javascript validation not working for only alphabetic values

I have used a javascript validation function to validate it. I've used it to see whether the text entered to the html textbox is alphabetic(No numeric characters allowed). The function is called during onkeyup and onblur. The only problem is even when numeric values or special characters are typed in the validation doesn't work. If I leave the field blank then it works(Displays that the field is left blank). Here's my javascript code:

function isAlphabetic(x,y){
    var exp = /^[a-zA-Z]+$/; 
    var a = document.getElementById(y).value;
    if(a=="" || a== null){
            document.getElementById(x).innerHTML = "You cannot leave this feild empty"; 
                return;
    }
    else if(a!="" && a!= null){
        if(y.match(exp)){
            document.getElementById(x).innerHTML = "";
            return;
        }
        else{
            document.getElementById(x).innerHTML = "Only enter alphabetic characters allowed";
            return;
        }

    }
    else{
        return;
    }