Pikuta, P.(Algebra and Discrete Mathematics, 2008)
Let q be a prime power and k∈{5,7,9,11}. In this paper it is shown that the girth of a graph D(k,q) is equal to k+5. As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of ...
The existence of a local solution to the Darboux problem uxy (x, y) = g (u (x, y)), u (x, 0) = u (0, y) = 0,
where g is Lebesgue measurable and has at most polynomial growth, is proved.