where can i find "older posts" on the bottom of the search page?

No. That’s the default WordPress theme and having access to an unedited version of the theme is vital when dealing with a range of site issues. First create a child theme for your changes.

Ah! Sorry – I misunderstood. The navigation is being generated by the twentyeleven_content_nav(() function in the parent theme. Try removing <?php twentyeleven_content_nav( 'nav-below' ); ?> from your child theme’s copy of search.php

Then you’ll need to create a custom version of twentyeleven_content_nav() in your child theme’s functions,php file. If you only want to use this custom wording in the search page, I’d suggest creating a completely new function – called something like my_search_nav() – and then replace <?php twentyeleven_content_nav( 'xxx' ); ?> with <?php my_search_nav( 'xxx' ); ?> in search,php.