The problem without inital conditions for semilinear ultraparabolic equation 

ut−λ(x,y,t)uy−∑i,j=1n(aij(x,y,t)uxi)xj+∑i=1nbi(x,y,t)uxi+c(x,y,t)u+g(x,t,u)=f(x,y,t)." role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">ut−λ(x,y,t)uy−∑ni,j=1(aij(x,y,t)uxi)xj+∑ni=1bi(x,y,t)uxi+c(x,y,t)u+g(x,t,u)=f(x,y,t).��−�(�,�,�)��−∑�,�=1�(���(�,�,�)���)��+∑�=1���(�,�,�)���+�(�,�,�)�+�(�,�,�)=�(�,�,�).

is researched in this paper. Conditions of existence and of uniqueness of general solution of this problem are obtained in class of functions with exponential behaviour if t→−∞" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">t→−∞�→−∞.