One of the most troublesome issues for the 9.3 million-member United Methodist Church has been its dwindling membership, a problem shared by other mainline Protestant denominations that has spawned a variety of commissions, task forces, studies and reports attempting to explain or reverse the trend.

A finding by two Duke University Divinity School researchers says the church should attack its problem by focusing less on the concerns of ethnic minorities and women and concentrate instead on the sharp regional differences that characterize the country's second largest Protestant denomination.

That is the view set forth by Robert L. Wilson and William H. Willimon in a newly published monograph entitled "The Seven Churches of Methodism."

United Methodism has been characterized as the most ubiquitous and most representative of American denominations, with Methodist congregations located in all but 3 percent of the counties of the United States.

"Methodism still is a national church," the authors of the new study write. They contend, however, that "the United Methodist Church is not one church, but seven" distinct regional churches. "To understand Methodism, the tensions and conflicts within the church and why it functions as it does, one must understand regional differences."

The church has lost 1.6 million members since 1968, when the Methodist Church merged with the considerably smaller Evangelical United Brethren to form the present United Methodist Church.

Last year's quadrennial General Conference authorized a special committee, headed by Bishop Richard B. Wilke of Arkansas, charged with doubling the membership by 1992.

But new statistics released last week on the rising death rate in the church emphasize what an uphill battle that promises to be. Between 1968 and 1983, the last year for which complete figures are available, 1.9 million church members died, a figure that exceeds the total net loss from all causes.

Furthermore, says the Rev. Warren J. Hartman, who directs research for the church's General Board of Discipleship, the death rate in the church, 13 per 1,000 in 1983, is the highest ever, and continues to inch up.

This indicator of an aging membership, combined with plummeting figures on Sunday schools, where the church has traditionally looked for a new generation of members, emphasizes the gravity of the crisis.

While the Wilson-Willimon study offers no solutions, the authors believe that it can help with a more realistic assessment of the problem. "I do think the church has got to look more seriously at regional differences . . . to attack the problem differently in different parts of the country," Wilson said in a telephone interview.

The study paints the bleakest picture for Methodism in New England and the industrial Northeast. In the Yankee church, "Methodism is facing a crisis of serious proportions," the authors say.

Between 1970 and 1982, the time interval used for the Wilson-Willimon study, membership in United Methodist churches decreased by 17.5 percent and the number of congregations dwindled by 6.7 percent. Even more alarming, the authors say, was the 48.5 percent decline in Sunday school attendance.

Never a strong force in this heavily Catholic area, today "Yankee Methodism is pessimistic," the authors claim, with some predicting the demise of the church there.

What the authors call the Industrial Northeast Church -- New York, Pennsylvania, New Jersey and down the Atlantic Coast to the Delmarva Penninsula, which includes Delaware and parts of Maryland and Virginia -- is in even worse shape.

In this stronghold of Methodism, membership has decreased by 22 percent, the number of churches by 7 percent and Sunday school attendance by 53 percent.

"To put it another way, every week for 12 years the United Methodist Churches in the Industrial Northeast lost 695 members," the study says.

Whites who once packed prestigious downtown First Churches moved to the suburbs, often leaving their religious ties behind. Southern blacks who crowded into cities such as New York, Philadelphia and Washington, were not attracted to the white-controlled church "even though the denomination considered itself to be on the forefront of racial justice issues," the authors say.

The healthiest of Methodism's seven churches, the authors say, are the Southwest Church -- Texas, Arkansas, Oklahoma and New Mexico -- and The Church South -- the 10 states of the southeastern United States.

Churches here not only benefit from the more religious orientation of Bible Belt culture, but Southern Methodism was a separate denomination for 95 years. Split off by the Civil War, the Southern church reunited with the Northern branch only in 1939.

The Southwest Church, where "a kind of boom mentality permeates the region and the church," the authors say, is the only regional church showing a net increase in membership -- 4.1 percent.

While there was a 3.8 percent membership loss during that period in The Church South, "The overall picture of Methodism in the south is more one of stability than of growth."

The authors hold that "Methodism is still strong in the Midwest" even though there has been a 10.8 membership loss overall, with the large urban church, which once provided a lot of the denominational leadership, particularly hard hit.

The Western Church, never a strong area, has suffered a 23 percent loss of membership, and Sunday school attendance was cut in half between 1970 and 1982.

In their conclusions, the authors say that in recent years, "Methodism has tended to ignore regional differences," concentrating instead on "groups based on race, language and gender, and attempted to compensate for past exclusion by bringing these persons into positions of leadership."

The authors contend that such emphasis is misplaced, with "less than one church member in 20 belong ing to a racial or cultural minority."

Douglas Johnson, research director for the national division of the denomination's Board of Global Ministries -- a post Wilson once held -- said the "basic data" of the report could be "useful" as "one of a whole series of things that will help the church focus attention and help solve its problems."

Less helpful, he said, is "some of the interpretation" of the church's emphasis on minorities "where it gets emotional and moves beyond what the data shows."