Worries about the glutted energy market pushed Dow members ExxonMobil and Chevron down by 3.4 percent each, leaving the blue-chip index in negative territory.
But Apple climbed 1.6 percent and Netflix 3.4 percent, suggesting a rotation by investors
Analysts were awaiting key earnings later in the week from Pfizer and Procter & Gamble, as well as major economic data releases, culminating with Friday's US jobs report for July.
The Dow Jones Industrial Average shed 0.2 percent to 8,404.51.
The broad-based S&P 500 dipped 0.1 percent to 2,170.84, while the tech-rich Nasdaq Composite Index rose 0.4 percent to 5,184.20.
SolarCity plunged 7.4 percent on news it agreed to be acquired by Tesla for $2.6 billion. Tesla dropped 2.0 percent. Analysts have cautioned that the deal could divert Tesla from its ambitious plan to expand production of electric cars.
Offshore driller Diamond Offshore sank 7.7 percent after reporting a second-quarter loss of $589.9 million following a large charge due to the slump in oil prices.
Biogen surged 4.1 percent and Ionis Pharmaceuticals 30.2 percent after announcing a successful clinical analysis of a treatment for spinal muscular atrophy.
Other biotech shares were also strong, with Gilead Sciences