What do you need a global declaration for in a class property? We're not dealing with plain functions here. $this->var1 will get you $var1 from any method inside the class, or from an instantiated object outside the class, where the variable is public. But let's be thorough...
Illustrating "Global"
Global has no meaning for class properties; although you can use it with variables inside class methods, just as you can do with regular functions. (But there are more elegant ways to get there; it's better to avoid a load of potentially hazardous clutter in the global scope.) Let's first define a variable:
$globby = 123; // Globby is a friend living outside a function.
A function that doesn't use a global declaration can neither access a variable from outside of its scope, nor change that variable's value. The story goes like this:
function foo() {
    echo $globby; // Here we have no clue who globby is?
    $globby = 321; // Here we define globby, but then he's totally forgotten. :(
}
foo(); // => 'Notice: Undefined variable: globby'
echo $globby; // => '123' ... still the same old globby.
However, a function that declares a variable as global can both access it and modify it outside the function's scope. Also, a variable newly defined as global inside the function is accessible outside it.
function foot() {
    global $globby; // Hey globby, won't you come on in! *Globby UFO Lands*
    echo $globby; // - Who are you? - I'm globby that says 123.
    $globby = 321; // - But I'm gonna tell you to say 321 everywhere.
}
foot(); // => '123' ... this here is the good old globby from the start.
echo $globby; // => '321' ... see, globby can change outside the function scope!
Illustrating "Static" in Classes
Be aware that static for a class property doesn't work like static for a function variable. Manual: "A static variable exists only in a local function scope, but it does not lose its value when program execution leaves this scope." And again: "Declaring class properties or methods as static makes them accessible without needing an instantiation of the class." (OOP Static Keyword; and Using Static Variables) Class properties retain their value for the lifetime of the object in any case. 
Now, to illustrate the usage (and non-usage) of static and non-static methods (aka. "class functions") and properties (aka. "class variables"). Let's make a little class:
class foo {
    static $one = 1; // This is a static variable aka. class property.
    var $two = 2; // But this is non-static.
    static function say_one() { // This is a static method.
        echo self::$one; // Uses self:: to statically access the property.
    }
    function say_two() { // This is a non-static method.
        echo $this->two; // Uses $this-> to dynamically access the property.
    }
}
Then let's see what works and what doesn't. Non-working options are commented out.
/* Static Variables and Methods */
echo foo::$one; // => '1'
echo foo::say_one(); // => '1'
// echo foo::$two; 
// => "Fatal error: Access to undeclared static property: foo::$two"
// echo foo::say_two(); 
// => "Strict: Non-static method foo::say_two() should not be called statically. 
// & Fatal error: Using $this when not in object context."
/* Non-Static Variables and Methods */
$f = new foo(); // This here is a real effin' instantiated dynamite object. *BOOM*
echo $f->two; // => '2' 
echo $f->say_two(); // => '2'
// echo $f->one; 
// => "Strict: Accessing static property foo::$one as non static. 
// & Notice: Undefined property: foo::$one."
echo $f->say_one(); // => '1'
Hope that clarifies. Note that you can access a static method via an instantiated object, and use that to access a static variable; but you can't directly access static variables as non-static without warnings.
Let me add a note on good practice. If you find that you need to be repeatedly declaring global variables inside your functions, or passing configuration parameters etc. as function arguments, it's a sign that you should probably be factoring your code into a class instead, accessing these globals as its properties. OOP is so much cleaner to work with. You'll code happier. $OOP->nirvana();.