Abstract:
For the equation $ ({\rm sign} y)|y|^{m}u_{xx}+u_{yy}+\alpha_{_{0}}|y|^{(m-2)/2}u_{x}+(\beta_{0}/y)u_{y}=0, $, considered in some unbounded mixed domain, uniqueness and existence theorems 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 are proved.
Keywords:unbounded domain, missing shift condition, analogue of the Frankl condition, non-Fredholm operator, isolated first-order singularity, singular integral equation, Wiener–Hopf equation, index, unique solvability.
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