Local and non-local boundary problems for mixed third order equation with string’s oscillation operator in hyperbolical part

In this work the existence and singularity of local and non-local boundary problems for equations of mixed types of the third order with multiple characteristics are proved. The singularity of solutions to these problems is set up by the method of integrals of energy and their existence - by the method of equivalent reduction to Fredholm`s integral equations of second kind.