Example:

class MyClass
{
    Composition m_Composition;

    void MyClass()
    {
        m_Composition = new Composition( this );
    }
}

I am interested in using depenency-injection here. So I will have to refactor the constructor to something like:

void MyClass( Composition composition )
{
    m_Composition = composition;
}

However I get a problem now, since the Composition-object relies on the object of type MyClass which is just created.

Can a dependency container resolve this? Is it supposed to do so?
Or is it just bad design from the beginning on?