Sorting an array of numbers in Java with an algorithm
Im impressed that you used selection sort. The standard bubble sort method would be slower. Have a look at the bubble sort method anyway.

int n = arr.length, r;
for (int i = 0; i &lt; n; i++) 
{
    for (int (j = i + 1); j &lt; n; j++) 
    {
        if (arr[i] &gt; arr[j]) 
        {
            r = arr[i];
            arr[i] = arr[j];
            arr[j] = r;
        }
    }
}


You could also have used the default Arrays.sort method

Arrays.sort(arr);


You are creating an applet. In this case, it would probably be good to declare the main method as static

When you are importing the packages, why have you imported the individual classes after importing them by wildcard character '*'; There is no need for it.
That is redundant and the computer wastes time re-importing and garbage-collecting. Just do:

import java.util.*;
import java.awt.*;
import java.awt.event.*; 
import javax.swing.*;


Also, printing mistake here:

String input_1 = JOptionPane.showInputDialog(frame, "How many numbers do you want to sort with SSSP ?");


Consider setting bounds to the buttons and text boxes in your mainframes, to make the locations more exact. That way, it will be easier to add a new GUI component to the window when you want to add it. 
The command goes:
&lt;name of object&gt;.setBounds(//x-axis from left, //y-axis from top, //width, //height)
For example:

t2 = new JTextField("Here are your sorted numbers : " + Arrays.toString(arr2));
t2.setBounds(20, 40, 75, 10);
main_frame.add(t2);

JButton buttonEnd = new JButton("Close application");
t2.setBounds(95, 40, 75, 10);
main_frame.add(buttonEnd);

JButton buttonRetry = new JButton("Try again !");
t2.setBounds(180, 40, 75, 10);
main_frame.add(buttonRetry);


WHY have you named your class AWTCounter? That makes me think you are counting numbers with certain properties or words in a sentence. Won't AWTSorter be better?

Great program though, especially if it's your first!