"struggle to resolve" is correct and usable in written English.
You can use it to describe a situation when someone is having difficulty in finding a solution to a problem. Example: The two sides have been struggling to resolve the dispute for weeks now.
One complaint we struggle to resolve regards women's sports coverage — or its relative dearth.
But in the background, the struggle to resolve Greece's financial crisis is likely to continue to unsettle investors.
The two younger Toprak children show a similar independence of thought as they struggle to resolve the contradictions that have brought their family down.
No easy answers, because these are questions that all of us – accusers, accused, professionals, police, politicians, media men, twitterers and compulsive gossips – need to struggle to resolve.
But there is also a more serious and nuanced point to be made here, which is that the tension between "doing" and "managing" is a genuine problem for many organisations, one that human-resources policies often struggle to resolve.
Sony's plans to marry its media content with a range of networked household electronic devices are fraught with a huge internal conflict that Sir Howard may struggle to resolve.
Quite what to, we are still struggling to resolve.
He has struggled to resolve his multiple, contradictory positions on the Iraq war.
Those talks are struggling to resolve several critical issues, people close to the discussions said.
We are all struggling to resolve our concern and our responsibility for our contributions.
Senior administration officials who have struggled to resolve the stalemate expressed relief at Mr. Gonzalez's arrival.
