Occidental Petroleum Corp. said yesterday its net income fell during the first quarter. The company said from Los Angeles that the decline was caused by a smaller gain from asset sales than in the year-earlier period.

In other earnings reports yesterday, PepsiCo Inc. said its first-quarter profits increased, and Eastman Kodak Co. announced a deep plunge from year-ago levels.

Occidental said its income was off 35.9 percent. It netted $74.2 million (46 cents a share), down from the first quarter of 1985, when it earned $115.7 million (45 cents).

The per-share earnings remained relatively stable because a preferred-stock buyback by Occidental slashed preferred dividends for the quarter to $21.9 million from its year-earlier level of $70.3 million.

Revenue declined nearly 2 percent to $3.63 billion from $3.7 billion, primarily because of lower prices for crude oil and natural gas, the company said.

The company's net included an after-tax gain of $24 million from the sale of some Australian operations. In the year-earlier period, it had an extraordinary gain of $100 million from the sale of holdings in the Dutch North Sea and California and from tax-loss benefits.

*PepsiCo Inc., the nation's second-largest soft-drink company, said its 9.4 percent increase in first-quarter profits occurred on a 10.4 percent gain in sales.

Net income rose to $68.7 million (79 cents a share) from $62.8 million (66 cents) in the same period a year ago.

Sales totaled $1.8 billion vs. $1.63 billion, it said.

Income from continuing operations rose 14 percent.

"These results were on target, and we expect that 1986 will be another year of substantial progress for PepsiCo," Chairman Donald M. Kendall said.

In addition to soft drinks, PepsiCo is in the snack foods and restaurant businesses.

Soft-drink earnings surged 20 percent on a 17 percent sales increase, spurred by the strongest international volume gains in more than five years and by U.S. volume increases, PepsiCo said.

*Eastman Kodak Co., in the first glimpse at its financial picture since the company's devastating fourth quarter and major layoffs, said profits plunged 58 percent from year-ago levels.

Sales in the first quarter rose to $2.35 billion from $2.13 billion in 1985, but costs associated with a massive employe reduction program cut earnings.

Net profits declined to $48.6 million (22 cents a share) from $115.2 million (50 cents) in the same period a year ago.

Kodak, which was under stress from its court-ordered ouster from the instant photography business in January, had reported a loss of $194 million in the fourth quarter. Earnings for 1985 slipped 64 percent to $332 million.

As a result, Chairman Colby Chandler vowed in February to cut the firm's worldwide work force by nearly 13,000 workers and to trim budgets by 5 percent.

In yesterday's statement, Kodak said it expects "solid gains in sales and operating earnings" for the rest of the year despite the cost of early retirements and severance packages for workers who are leaving.