Solution number three:

• Store whitelisted domains in mapping (string => bool) whitelisted
• Find out if a given domain is whitelisted, using if (whitelisted[domain])

modifier contains (string memory what, string memory where) {
    bytes memory whatBytes = bytes (what);
    bytes memory whereBytes = bytes (where);

    require(whereBytes.length >= whatBytes.length);

    bool found = false;
    for (uint i = 0; i <= whereBytes.length - whatBytes.length; i++) {
        bool flag = true;
        for (uint j = 0; j < whatBytes.length; j++)
            if (whereBytes [i + j] != whatBytes [j]) {
                flag = false;
                break;
            }
        if (flag) {
            found = true;
            break;
        }
    }
    require (found);

    _;
}

function foo (string memory str) public contains ("solidity", str) {
    ...
}

You can use the ASCII codes to do so:

function testStr(string str) public pure returns (bool){
    bytes memory b = bytes(str);
    if(b.length > 13) return false;

    for(uint i; i<b.length; i++){
        bytes1 char = b[i];

        if(
            !(char >= 0x30 && char <= 0x39) && //9-0
            !(char >= 0x41 && char <= 0x5A) && //A-Z
            !(char >= 0x61 && char <= 0x7A) && //a-z
            !(char == 0x2E) //.
        )
            return false;
    }

    return true;
}

You can compare strings by hashing the packed encoding values of the string:

if (keccak256(abi.encodePacked(a)) == keccak256(abi.encodePacked(b))) {
  // do something
}

keccak256 is a hashing function supported by Solidity, and abi.encodePacked() encodes values via the Application Binary Interface.