How to display the date in the input after the query

As your goal and submit the dates after the query you can retrieve this data by the variable post as shown below. If you have doubts about a var_dump ($ _ POST) and you will see all the post you made

<?php include "conexao.php"; ?>
        <form class='navbar-form navbar-left' action='#'>
            DATA INICIAL:&nbsp; &nbsp; <input type='text' name='datainicio' id='datainicio' value="<?php echo $_POST['datainicio']?>" class='form-control'>
            DATA FINAL :&nbsp; &nbsp; <input type='text' name='datafinal' id='datafinal' <?php echo $_POST['datafinal']?>class='form-control'>

            OCORRENCIA :&nbsp; &nbsp; <select class='form-control' id='ocorrencia' name='ocorrencia'>

                <?php
                $result = mysql_query("SELECT * FROM  ocorrencias") or die("não foi possivel fazer a pesquina no banco");
                while ($row    = mysql_fetch_assoc($result))
                {
                    $v_oc_id   = $row["oc_id"];
                    $v_oc_desc = $row["oc_desc"];
                    echo"<option value='$v_oc_id'>$v_oc_desc</option>";
                }
                ?>
            </select>
            <button type='submit'class='btn btn-primary'><span class='  glyphicon glyphicon-search'></span></button>
        </form>

        ?>

<?php
include "conexao.php";

$datainicio='';
if(isset($_POST["datainicio"])){ $datainicio = $_POST["datainicio"]; }

$datafinal='';
if(isset($_POST["datafinal"])){ $datafinal = $_POST["datafinal"]; }

    echo"<form class='navbar-form navbar-left' action='#'>";
      echo"DATA INICIAL:&nbsp; &nbsp; <input type='text' name='datainicio' value='$datainicio' id='datainicio' class='form-control'>";
      echo"DATA FINAL :&nbsp; &nbsp; <input type='text' name='datafinal' value='$datafinal' id='datafinal'class='form-control' >";
      echo"OCORRENCIA :&nbsp; &nbsp; <select class='form-control' id='ocorrencia' name='ocorrencia'>";

            $v_oc_desc = 'v_oc_desc';
            echo"<option value='$v_oc_id'>$v_oc_desc</option>";        

        echo"</select>";
        echo"&nbsp; &nbsp; <button type='submit'class='btn btn-primary'><span class='  glyphicon glyphicon-search'></span></button>";
echo"</form>";

 ?>

You can retrieve the data in the following way, as already mentioned in previous answers, through the global variable $_POST .

Regarding the error mentioned in the comments in the previous answer:

<br/><b>Notice</b>: Undefined index: datafinal in<b>/var/www/html/sistema/principal.php</b> on line <b>134</b><br/>, "como se inicia sem data retorna isso, e mesmo após a consulta continua retornando isso"

In order to avoid this, you can first define the variables of type string with a blank space 'espaço' , note not enough simple single quotes space is needed.

<?php
include "conexao.php";

$datainicio=' ';
if(isset($_POST["datainicio"])){$datainicio = $_POST["datainicio"];}
$datafinal=' ';if(isset($_POST["datafinal"])){$datafinal = $_POST["datafinal"];} 
    echo"<form class='navbar-form navbar-left' action='#' method='post'>";
    echo"DATA INICIAL:&nbsp; &nbsp; <input type='text' name='datainicio' id='datainicio' value='".$datainicio."' class='form-control'>";
    echo"DATA FINAL :&nbsp; &nbsp; <input type='text' name='datafinal' id='datafinal' value='".$datafinal."' class='form-control'>";
    echo"OCORRENCIA :&nbsp; &nbsp; <select class='form-control' id='ocorrencia' name='ocorrencia'>";

    $result= mysql_query ("SELECT * FROM  ocorrencias") or die ("não foi possivel fazer a pesquina no banco");
    while($row = mysql_fetch_assoc($result))
    {
        $v_oc_id   = $row["oc_id"];
        $v_oc_desc = $row["oc_desc"];
        echo"<option value='$v_oc_id'>$v_oc_desc</option>";        
    }

    echo"</select>";
    echo"<button type='submit'class='btn btn-primary'><span class='glyphicon glyphicon-search'></span></button>";
    echo"</form>";
?>

Take a little time, with this question: #