The Gevrey Problem for a One-Dimensional Third Order Equation with Changing Time Direction

摘要

We consider a Gevrey problem for a third-order equation with multiple characteristics with weighted gluing conditions. In the case of continuous gluing conditions, the solvability of the Gevrey problem is reduced to the theory of integral equations with a kernel that is homogeneous of degree -1, and in the case of weighted gluing conditions the solvability is reduced to the theory of singular integral equations with a singular kernel. The solvability of boundary value problems is established in Holder spaces. It is shown that the Holder classes of solutions of the Gevrey problem in the case of weighted gluing functions depend both on the non-integer Holder exponent and on the weight coefficients of the gluing conditions when necessary and sufficient conditions are satisfied for the input data of the problem.