Minister John N. Oswalt argues for a single author of Isaiah.
John Oswalt, "Authorship and Date," The Book of Isaiah, Chapters 1-39 (Grand Rapids: Eerdmans Publishing, 1986) 23-27
Yet another argument that must be lodged against the hypothesis of multiple authorship of Isaiah is the fact that it has not been able to produce any unanimity of results. While the work of Holladay noted above is one example of how the process is supposed to have worked, there would be almost no scholar who would agree with many of the details of his contentions. Although biblical studies are far from being an exact science, it is still true that if a methodology is correct, it ought to yield substantially similar results in the hands of different researchers. In fact, that is not the case with the study of Isaiah. Two commentators who both share a commitment to form criticism and to multiple authorship of Isaiah may vary by as much as three hundred years as to when a particular unit was written. There is something wrong with a methodology that cannot yield more predictable results.
One of the more interesting pieces of evidence is the even distribution of the phrase "the Holy One of Israel" throughout the book. This phrase only occurs thirty-one times in the Old Testament, and no fewer than twenty-five of these are in Isaiah, with twelve occurrences appearing in chapters 1-39 and thirteen appearing in chapters 40-55.
Another evidence of the single authorship of the book is the absence of specific historical references for the exilic and postexilic periods. When the book of Isaiah is compared to Ezekiel or to Malachi, these differences become obvious. Whereas it is typical among the Hebrew prophets to root their oracles in specific events and circumstances, and whereas this feature is present in chapters 6-39 of Isaiah, there is almost none of this kind of material in chapters 40-66.
Three possible explanations present themselves: (1) The author did not know this information; (2) the author knew it but did not include it; (3) the author originally included it, but it was removed for some reason. If the author of the material was Isaiah, then the facts are easily explicable. Isaiah knew the general circumstances of the exilic and postexilic periods, but apart from the one startling fact of the name of the deliverer Cyrus, he knew no other details. On the one hand, if the author was writing at the time of the events and knew the details, as in the case of Cyrus, there is no obvious reason to make the rest of his presentation so ahistorical, On the other hand, if the details were originally there but were suppressed in all cases but the reference to Cyrus, then we again are faced with editors who want us to believe Isaiah of Jerusalem is responsible for the whole book while they know that is untrue.