Undated (AP) _ Merrill Lynch & Co. and PaineWebber Group Inc. reported Monday their earnings declined in the third quarter, while another large securities firm, Bear Stearns Cos. Inc., said its fiscal first-quarter profit rose over a year ago.

Meanwhile, Charles Schwab Corp., a San Francisco-based discount brokerage firm, said it had a sharp earnings increase in the three months ended Sept. 30. Merrill Lynch, based in New York, said net income from continuing operations fell to $43.2 million, or 36 cents per share, from $56.1 million, or 49 cents, in 1988. Revenue rose 10 percent to $2.8 billion from $2.6 billion.

Bear Stearns, of New York, said first-quarter earnings totaled $22.1 million, or 23 cents a share, compared with earnings of $20.5 million, or $20 cents, in the same period last year. Revenue rose 21 percent to $580.4 million from $478.9 million in 1988.

PaineWebber, also of New York, said third-quarter earnings totaled $16.83 million, or 41 cents per share, on revenue of $444.87 million. That compared with earnings of $20.92 million, or 50 cents a share, in 1988.

Merrill Lynch said the third-quarter results ''reflected an industry-wide softness in some of our core business activities.''

''The lower volume of underwritng activity and principal transactions were partially offset by revenue increases from commissions and asset management fees,'' the company said in a statement.

For the first nine months of this year, Merrill Lynch said it earned $144.4 million from continuing operations, or $1.23 a share, compared with a profit of $164.1 million , or $1.45 a share, in 1988.

Bear Stearns Chairman Alan C. Greenberg said he was pleased with the first- quarter results ''because several of our departments ... were operating in a very difficult environment.''

He said the company saw a decline in principal transactions during the quarter due to a drop in government bond trading activities, among other things.

PaineWebber said third quarter results included a broad-based improvement in core businesses. It said the 1988 results included a pretax gain of $46.3 million, and without that, the quarter would have shown a loss.

For the first nine months of 1989, PaineWebber's earnings totaled $41.09 million, or 85 cents a share, on revenue of $1.27 billion. That compared with earnings of $41.84 million, or 77 cents, and $1.30 billion in revenue, during the same period last year.

Schwab said it earned $4.6 million, or 16 cents a share, in the third quarter on $142.1 million in revenue. That was up from earnings of $2.7 million, or 10 cents a share, and revenue of $98 million.

For the first three quarters, Schwab earnings rose to $12.8 million, or 46 cents a share, from $6.8 million, or 25 cents. Revenue totaled $185.6 million, up from $158.4 million.