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A MAJORANT CRITERION OF THE FIRST ORDER FOR THE TOTAL PRESERVATION OF GLOBAL SOLVABILITY OF A CONTROLLED HAMMERSTEIN TYPE EQUATION

Annotation

We consider a nonlinear functional operator equation of the Hammerstein type as a convenient form for describing a wide class of controlled distributed parameter systems. For the equation under study we formulate a majorant criterion of the total (with respect to the whole set of admissible controls) preservation of global solvability. This criterion uses the hypotheses on Volterra property of the operator component and on differentiability with respect to the state variable of the functional component in the right-hand side of the equation. Moreover, it is based on hypotheses consisting in the global solvability of a certain majorant equation, and also of the initial one for a some fixed admissible control.

Keywords

functional operator equation of the Hammerstein type; total preservation of global solvability; majorant equation; Volterra property

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UDC

517.988 + 517.977.56

Pages

1526-1529

References

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Received

2015-05-05

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Scientific articles

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