The Gevrey boundary value problem for a third order equation

We consider the Gevrey and Cauchy problems 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 homogeneous integral equations of degree -1 with a kernel. 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 Hölder spaces. It is shown that the Hölder classes of solutions of the Gevrey problem in the case of weighted gluing functions depend both on the non-integer Hölder exponent and on the weight coefficients of the gluing conditions when necessary and sufficient conditions are satisfied for the input data of the problem.