Abstract
The solvability of a boundary value problem for the differential equation \(h\left( x \right){u_t} + {\left( { - 1} \right)^m}\frac{{{\partial ^{2m + 1}}u}}{{\partial {a^{2m + 1}}}} - {u_{xx}} = f\left( {x,t,a} \right)\) is studied in the case where h(x) has a jump discontinuity and reverses its sign on passing through the discontinuity point. Existence and uniqueness theorems are proved in the case of solutions having all Sobolev generalized derivatives involved in the equation.
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