A book ( [Gordon92Battleships] ) of puzzles has been published.
Fathom It! [FathomIt] is a shareware program for playing and solving these puzzles. This gives you a program to let you solve puzzles on screen, as well as a rule-based solver. The trial version contains 80 puzzles: 10 each in four levels of difficulty and two sizes (7x7 and 10x10.) The full version contains thousands. All puzzles distributed can be solved by the rule based solver without backtracking. However puzzles exist that it cannot solve (see the overview page).
Puzzle—Solving the Battleship Puzzle as an Integer Programming Problem
INFORMS Transactions on Education 10(3), 156-162, 2010
Constraint Programming Models for Solitaire Battleships
Technical Report 20-2006, CP Pod, 2006
Solitaire Battleships : 108 Challenging Logic Puzzles