Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 755-760
Local solutions to Darboux problem with a discontinuous right-hand side
(Marie Curie-Skłodowska University, Institute of Mathematics pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland)
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.
Darboux problem, discontinuous differential equations