The first lines of Ralph Ellison's novel Invisible Man are very comparable to the first lines of Dostoevksy's novella Notes from Underground. In Dostoevsky's novel, they go like this:
I am a sick man . . . I am a spiteful man. I am an unattractive man. I believe my liver is diseased. However, I know nothing at all about my disease, and do not know for certain what ails me. I don't consult a doctor for it, and never have, though I have a respect for medicine and doctors. Besides, I am extremely superstitious, sufficiently so to respect medicine, anyway (I am well-educated enough not to be superstitious, but I am superstitious). No, I refuse to consult a doctor from spite. That you probably will not understand. Well, I understand it, though. Of course, I can't explain who it is precisely that I am mortifying in this case by my spite: I am perfectly well aware that I cannot "pay out" the doctors by not consulting them; I know better than anyone that by all this I am only injuring myself and no one else. But still, if I don't consult a doctor it is from spite. My liver is bad, well--let it get worse!
In Ellison's novel, the first lines in the Prologue are as follows:
I am an invisible man. No, I am not a spook like those who haunted Edgar Allan Poe; nor am I one of your Hollywood-movie ectoplasms. I am a man of substance, of flesh and bone, fiber and liquids—and I might even be said to possess a mind. I am invisible, understand, simply because people refuse to see me. Like the bodiless heads you see sometimes in circus sideshows, it is as though I have been surrounded by mirrors of hard, distorting glass. When they approach me they see only my surroundings, themselves, or figments of their imagination—indeed, everything and anything except me.
In both passages, there is a declaration of self-awareness and attempts by each speaker to explain their respective conditions to an imaginary listener. They describe how these conditions have impacted their responses to their respective societies. The Underground Man is so consumed by "spite" that he refuses the assistance of those who could help him. In this instance, the narrator is rejecting a facet of society (the educated bourgeoisie, represented here by doctors) to arm himself against a belief that he'll inevitably be rejected anyway. In Ellison's novel, the narrator has already been rejected: others refuse to see him as a fully realized human being.
In Dostoevsky's novella, the problem is internal: it is a disease that racks that narrator. In Ellison's, the problem is external: he has become distorted by others' imaginations and by surrounding conditions that he neither created nor controls.
Ellison's novel uses the existential problem that Dostoevsky presents: that isolation results from an inability to live with others. In the case of Dostoevsky's Underground Man, insecurity is fostered by resentment. In the case of Ellison's narrator, it's fostered by racism.