Nathan Summerfield, left, is a "person of interest" in the disappearance of his former girlfriend, Lynn Jackenheimer, right, who was last seen vacationing with her children on North Carolina's Outer Banks. (Ashland County Sheriff's Office)

Authorities say 33-year-old Lynn Jackenheimer of Ashland went to the Outer Banks of North Carolina last week with her boyfriend, Nate Summerfield, and her two children, but didn't return with them. Summerfield's brother called police to say Summerfield told him he strangled the woman.

Police said Summerfield, 27, returned his girlfriend's children to Ohio Sunday and left them with his family. He then withdrew money from an ATM, ditched his cellphone along a road in Ashland County and vanished, Fox8.com reported.

As of late Tuesday, authorities said they had no solid evidence a crime was committed, the report said. Though authorities acknowledge that as more time passes without finding her, the more troubling the case becomes.

"It's hard. The longer it goes the worse it is," Carl Richert, the captain from Ashland Sheriff’s Department, said. "It's frustrating for us because we are trying to do everything we can."

Dare County Sheriff's Office in North Carolina, where the couple vacationed, said it's assisting in the investigation.

Steve Hoggard, the chief deputy of the Dare County Sheriff’s Office, told FoxNews.com that authorities have been searching beaches and roads where the couple recently stayed.

Hoggard described some beach areas as challenging because of the thick scrub brush in some areas.

"Some of these beaches are perfect spot to dump something you don't want somebody to find," he said. He said local authorities are keeping an eye out for the person of interest and trying to contact anyone who may know the couple, since they vacationed at the area a few times before.

Jackenheimer works at Beer Barrel in Ashland and did not report to work on Monday, Dean Emmons, her boss, said. He offered $1,000 of his own money as a reward to find Jackenheimer and Summerfield.

Summerfield was convicted of domestic violence in 2009, after records show he choked Jackenheimer, pinned her to a table and dragged her through the house by her neck, Fox8.com reported. In related court documents, Jackenheimer said she was “scared of him.” Summerfield is a person of interest in a missing persons report.

The two children, ages 3 and 13, are not much help with the investigation because they have been largely “kept in the dark” about a lot of things,” Richert told Fox8.com. Relatives said the children understand their mom is missing.

"This morning they asked us to go find Mommy for them," said Raymond Johnson, Jackenheimer’s stepfather. "[The 3-year-old] got up this morning wanting us to go find Mommy for him. He sits and cries wanting his Mommy. Give her back to him, would you please do the right thing Nate?"

Source: foxnews.com