START CONTROL OF POSITIVE SOLUTIONS TO SOBOLEV TYPE EQUATIONS

N. N. Solovyova, S. A. Zagrebina, G. A. Sviridyuk

Abstract


Using degenerate holomorphic groups of operators generated by linear continuous operators L and M, a positive solution to a linear homogeneous Sobolev type equation is obtained; necessary and sufficient conditions for the positivity of these groups are found. Start control of positive solutions to the Showalter–Sidorov problem is investigated.

Keywords


start control problem; positive solutions; initial problem; abstract homogeneous Sobolev type equation

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