insert multiple authors only if it exists in MySQL
As this is a m:n relationship you'd need an intermediate table that links authors to papers, e.g.:

CREATE TABLE paper_author (
  paper_id INT,
  author_id INT,
  PRIMARY KEY(paper_id, author_id)
);


Then you can check for all authors of a paper with:

SELECT paper.name, author_name 
  FROM paper
  JOIN paper_author ON paper.id = paper_author.author_id
  JOIN author       ON paper_authors.author_id = author.id
 WHERE paper.name = ...;


Same for all papers by a specific author with

 WHERE author.name = ...;


Or if you you want a list of authors for each paper on a single row you can use GROUP BY and the GROUP_CONCAT() aggregate function:

SELECT paper.name, GROUP_CONCAT(author_name)
  FROM paper
  JOIN paper_author ON paper.id = paper_author.author_id
  JOIN author       ON paper_authors.author_id = author.id
 GROUP BY paper.name;