A Problem with Analogue of the Frankl and Mixing Conditions for the Gellerstedt Equation with Singular Coefficient

Abstract

For the equation \((\operatorname{sgn} y){{\left| y \right|}^{m}}{{u}_{{xx}}} + {{u}_{{yy}}} + {{\alpha }_{0}}{{\left| y \right|}^{{(m - 2)/2}}}{{u}_{x}} + ({{\beta }_{0}}{\text{/}}y){{u}_{y}} = 0,\) considered in some unbounded mixed domain, uniqueness and existence theorems are proved for a solution to the problem with the missing shift condition on the boundary characteristics and an analogue of the Frankl-type condition on the interval of degeneracy of the equation.