is there any linux application that don't uses the libc ?

gawd knows, try looking at the dependencies of random programs!

Apart from the kernel and libc itself, virtually none.

but when i compile a program are still necessary the library?

In short: yes, you need libc.

However, it is possible, as the kernel and libc can be compiled, right?
But is is difficult. Even with this program:
if you compile it the normal way, say "gcc -o donothing donothing.c", then it gets linked with libc. You can check this with "ldd donothing".

There are command line options to gcc for not-linking in the standard libs. (check man gcc for -nostdlib or -nodefaultlibs). But I tried it, and it's not that easy. When you compile with (one of) these options, gcc doesn't even know how to get the program started anymore...

There is a website about creating tiny executables, (at least) some of which don't need libc, but they are using assembly. See:
http://www.muppetlabs.com/~breadbox/software/tiny/

Purhaps some sites about embedded systems have some info for you. Try googling for that.

Why do you want to do this, anyway?

I don't know if you already know this but here it is :

libc isn't neccesary, it's necesary at compile time, cause it has the info that is needed by the program to 'do things'.

If I do a:

printf("Hi\n");

The way of do that printf in 'computer languaje' is stored in glibc. But when I'm making a binary of that you can choise if you want to make it to search on the libc (glibc, culibc, etc) or store it in the binary itself.

Making a big binary, with all the instructions inside, its called static.
Making a small binary, that has the direction of where are the instructions (glibc) is called shared.

The pros and cons: When using a static binary you don't need anything else. But the functions inside it, the store 'ways of do things' inside, are never gonna be actualized. Also the binary use to be to mouch big in filesize. The shared way (the stantard of the distros for distribute binarys) need some run time dependencis, glibc basic, mostly, if it needs other lib, like libpng for example, libpng also is gonna to need glibc.

I hope this is usefull in any way.

But note that static linking can open a security hole. When a bug / security hole is discovered in a library, you can update the library to close the hole, but static linked binaries will still use there own statically linked version, including the hole.

Also, not only the size of the executable increases when linked statically, but also the memory footprint when it runs.

Yes I ommit that cause I don't think necesary but is true.