How to show search results in view within panels?
If I understand the question correctly, you would like to send users from a search form to a specific (custom) search results page (which happens to also have some other panels etc on it).

I do not believe the panels/page manager aspect really affects how the search box operates, in which case all we have to do is specify where you would like the search form to send the user.

The following code (for an imaginary module entitled customsearch just found existing module entitled custom_search, not related). 


creates a block to hold a search form (you can then place this wherever you want)
constructs a simple textfield search form to go in the block
defines a custom submit to pass the search argument to your customised search results page


1)

// Implements hook_block_view().
function customsearch_block_view($delta = '') {
  if (user_access('search content')) {
    $block['content'] = drupal_get_form('customsearch_block_form');
    return $block;
  }
}


2)

// Implements hook_forms().
function customsearch_forms() {
  $forms['customsearch_block_form']= array(
    'callback' =&gt; 'customsearch_box',
    'callback arguments' =&gt; array('customsearch_block_form'),
  );
  return $forms;
}

// Form builder; Output a search form for the search block's search box.
function customsearch_box($form, &amp;$form_state, $form_id) {
  $form['customsearch_form'] = array(
    '#type' =&gt; 'textfield',
    '#title' =&gt; '',
    '#title_display' =&gt; 'invisible',
    '#default_value' =&gt; '',
    '#attributes' =&gt; array(
      'title' =&gt; t('Search the website'), 
      'placeholder' =&gt; t('search the website'),
    ),
  );
  $form['actions'] = array('#type' =&gt; 'actions');
  $form['actions']['submit'] = array('#type' =&gt; 'submit', '#value' =&gt; t('Search'));

  // define function to determine search destination
  $form['#submit'] = array('customsearch_search_box_form_submit');

  return $form;
}


3)

// overide submission of search query from block
function customsearch_search_box_form_submit($form, &amp;$form_state) {
  $searchterm = $form_state['values']['plus_search_form'];
  $search_path = 'specialcustomsearch'// replace with the path to your search results page
  // pass search term to your search results page as argument
  drupal_goto($searchpath .'/'. $searchterm);
}