Question: What inspired this film named "Inside Llewyn Davis"?
About the article "Inside Llewyn Davis", section "Production".

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12 Years a Slave  "American Hustle"  "Gravity"  "Her"  "Inside Llewyn Davis"  
In February 1961, Llewyn Davis (Oscar Isaac) is a struggling folk singer in New York City's Greenwich Village.
His musical partner, Mike Timlin, has committed suicide; his recent solo album "Inside Llewyn Davis" is not selling; he has no money and is sleeping on the couches of friends and acquaintances.
After performing in the Gaslight Cafe, Llewyn is beaten up by a shadowy suited man for heckling the previous night.
He sleeps at the apartment of his older friends, the Gorfeins.
When he leaves the next morning, the Gorfeins' ginger cat escapes.
Llewyn takes the cat to the apartment of his friends Jim (Justin Timberlake) and Jean (Carey Mulligan) Berkey.
Jean tells him she is pregnant, and fearing that Llewyn may be the father, asks him to pay for an abortion.
After he sleeps on their couch, the Gorfeins' cat escapes again.
On Jim's invitation, Llewyn, as part of the "John Glenn Singers", records a novelty song with Jim and Al Cody (Adam Driver).
Needing money immediately, Llewyn agrees to $200 with no royalties.
At the gynecologist's office, Llewyn sets up Jean's appointment and discovers that a previous girlfriend, whose abortion he also paid for, decided to keep the baby and move to Akron without telling him.
Llewyn and Jean argue about his lack of direction.
He spots what he believes to be the Gorfeins' cat and returns it that evening.
Asked to play after dinner, he reluctantly performs "Fare Thee Well", a song he had recorded with his deceased partner Mike.
When Mrs. Gorfein starts to sing Mike's harmony, Llewyn snaps.
Mrs. Gorfein leaves the table crying, then returns with the cat, having realized that it is not theirs.
Llewyn leaves with the cat.
Llewyn rides with two musicians driving to Chicago: the laconic beat poet Johnny Five (Garrett Hedlund) and the odious jazz musician Roland Turner (John Goodman).
At a roadside restaurant, Roland collapses from a heroin overdose.
The three stop on the side of the highway to rest.
When a police officer tells them to move on, Johnny resists and is arrested.
Without the keys, Llewyn abandons the car, leaving the cat and the unconscious Roland behind.
In Chicago, Llewyn auditions for Bud Grossman (F. Murray Abraham).
Grossman says Llewyn is not suited to be a solo performer but suggests he might incorporate him in a new trio he is forming.
Llewyn rejects the offer and hitchhikes back to New York.
Driving, he hits what he fears may be the same cat.
In New York, he pays $148 in back dues to rejoin the merchant marine union, and visits his ailing father.
Llewyn searches for his seaman's license so he can ship out with the merchant marines, but his sister has thrown it out.
At the Gaslight, Pappi claims he had sex with Jean.
Llewyn becomes upset (presumably at feeling he was swindled by Jean for abortion money) and heckles a woman as she performs.
He goes to the Gorfeins' apartment, where they graciously welcome him.
He is amazed to see that their actual cat, named Ulysses, has found his way home.
The scene from the beginning of the film then replays.
Llewyn performs at the Gaslight.
Pappi teases him about his heckling the previous evening and tells him that a friend is waiting outside.
As Llewyn leaves the building, a young and unknown Bob Dylan takes the stage and begins to sing.
Behind the Gaslight, Llewyn is beaten by the shadowy suited man for heckling the previous night's performer, his wife.
He watches as the man leaves in a taxi and quietly bids him "au revoir". 
The Gate of Horn appears in the 2013 film Inside Llewyn Davis; its exterior as a visual effect with a set construction interior. 
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Joel and Ethan Coen – "Inside Llewyn Davis" <br>2.
Alfonso Cuarón – "Gravity" <br>3.
Steve McQueen – "12 Years a Slave" 
Gravity — Emmanuel Lubezki "12 Years a Slave" — Sean Bobbitt "The Great Gatsby" — Simon Duggan "Inside Llewyn Davis" — Bruno Delbonnel "Nebraska" — Phedon Papamichael