Rendering partial view on button click in ASP.NET MVC

Change the button to

<button id="search">Search</button>

and add the following script

var url="https://stackoverflow.com/questions/29142422/@Url.Action("DisplaySearchResults", "Search")";
$('#search').click(function() {
  var keyWord = $('#Keyword').val();
  $('#searchResults').load(url, { searchText: keyWord });
})

and modify the controller method to accept the search text

public ActionResult DisplaySearchResults(string searchText)
{
  var model = // build list based on parameter searchText
   return PartialView("SearchResults", model);
}

The jQuery .load method calls your controller method, passing the value of the search text and updates the contents of the <div> with the partial view.

Side note: The use of a <form> tag and @Html.ValidationSummary() and @Html.ValidationMessageFor() are probably not necessary here. Your never returning the Index view so ValidationSummary makes no sense and I assume you want a null search text to return all results, and in any case you do not have any validation attributes for property Keyword so there is nothing to validate.

Edit

Based on OP’s comments that SearchCriterionModel will contain multiple properties with validation attributes, then the approach would be to include a submit button and handle the forms .submit() event

<input type="submit" value="Search" />

var url="https://stackoverflow.com/questions/29142422/@Url.Action("DisplaySearchResults", "Search")";
$('form').submit(function() {
  if (!$(this).valid()) { 
    return false; // prevent the ajax call if validation errors
  }
  var form = $(this).serialize();
  $('#searchResults').load(url, form);
  return false; // prevent the default submit action
})

and the controller method would be

public ActionResult DisplaySearchResults(SearchCriterionModel criteria)
{
  var model = // build list based on the properties of criteria
  return PartialView("SearchResults", model);
}