The phrase "ability to solve their" is correct and usable in written English.
It can be used when discussing someone's skills or competencies in addressing problems or challenges.
Example: "The team's ability to solve their issues quickly has greatly improved our project timelines."
Alternatives: "capability to address their" or "skill in resolving their".
Some governments have discovered that once they entered Chapter 9 it did not make much difference in their ability to solve their problems.
Working-class people in this region overwhelmingly backed George W. Bush in 2000 and 2004 but then lost faith in the Republican Party's ability to solve their problems.
The New Jersey-based outfit is making headway, in the process showing that neither Japan's banks nor its financial authorities has the ability to solve their problems by themselves.
"I see kids from unemployed homes, broken homes, as having more stress and less ability to solve their problems," said Jay McCormick, head counselor at Peoria High School.
This is communicating to them -- regularly -- that we believe in them and we believe in their ability to solve their own problems.
The advertisement focused on solidarity among women and on their ability to solve their 'intimate problems' by using the advertised preparation.
However, the hypothesis underlying PST, that emotional symptoms are generally induced by problems of living; its object, to increase patients' abilities to solve their problems; and provide a means to achieve this – six structured sessions with a therapist – completely rely on shared notions of legitimate conduct, and co-operation within clinical encounters.
Understand the fact that they are reaching you as they trust you and your abilities to solve their problems.
They also explained how their ability to solve problems enhanced their clinical thinking.
The British people appear to have lost faith in the ability of Westminster to solve their problems.
Moving into a meeting room, Xi, speaking first and sitting opposite Ma, said Chinese people on the two sides of the Taiwan Strait had the ability and wisdom to solve their own problems.
