in mobile application how to do selectmenu-custom-filter using jquery mobile

I have a few select menus of jquery-mobile in my project. Now the list is so large and i have to put search option in it for filtering. I searched it in jquery mobile but did not find the solution in it. Please help me and let me know is it possible or not.

I find it small list select menu custom filter, but those are opening in separate page, like select menu one page and options is opening in another page like that i got it and also look and feel also not good some time coming mobile native option list type is coming when click on filter menu option. but i don't want that on which page is have select menus i need to display on that page like popup box and if select menu is larger than the screen height in that fields i need to give certain height only for that filter menu and give to scroll option.Help me any one

i have this country menu list in country page and also other option also there like city,states etc.

      <select name="demo" id="demo" data-native-menu="false" class="filterable-select">
            <option value="AL">Alabama</option>
            <option value="AK">Alaska</option>
            <option value="AZ">Arizona</option>
            <option value="AR">Arkansas</option>
            <option value="CA">California</option>
            <option value="CO">Colorado</option>
            <option value="CT">Connecticut</option>
            <option value="DE">Delaware</option>
            <option value="FL">Florida</option>
            <option value="GA">Georgia</option>
            <option value="HI">Hawaii</option>
            <option value="ID">Idaho</option>
            <option value="IL">Illinois</option>
            <option value="IN">Indiana</option>
            <option value="IA">Iowa</option>
            <option value="KS">Kansas</option>
            <option value="KY">Kentucky</option>
            <option value="LA">Louisiana</option>
            <option value="ME">Maine</option>
            <option value="MD">Maryland</option>
            <option value="MA">Massachusetts</option>
            <option value="MI">Michigan</option>
            <option value="MN">Minnesota</option>
            <option value="MS">Mississippi</option>
            <option value="MO">Missouri</option>
            <option value="MT">Montana</option>
            <option value="NE">Nebraska</option>
            <option value="NV">Nevada</option>
            <option value="NH">New Hampshire</option>
            <option value="NJ">New Jersey</option>
            <option value="NM">New Mexico</option>
            <option value="NY">New York</option>
            <option value="NC">North Carolina</option>
            <option value="ND">North Dakota</option>
            <option value="OH">Ohio</option>
            <option value="OK">Oklahoma</option>
            <option value="OR">Oregon</option>
            <option value="PA">Pennsylvania</option>
            <option value="RI">Rhode Island</option>
            <option value="SC">South Carolina</option>
            <option value="SD">South Dakota</option>
            <option value="TN">Tennessee</option>
            <option value="TX">Texas</option>
            <option value="UT">Utah</option>
            <option value="VT">Vermont</option>
            <option value="VA">Virginia</option>
            <option value="WA">Washington</option>
            <option value="WV">West Virginia</option>
            <option value="WI">Wisconsin</option>
            <option value="WY">Wyoming</option>
        </select>