The Russian war against Ukraine will inevitably dominate the summit of G7 nations in Bavaria.

And the leaders of the US, UK, Germany, France, Italy, Canada and Japan face a difficult challenge.

They are aiming to put on a show of unity and resolve over the war. In recent months, the Western alliance has shown signs of strain and fatigue.

Some voices - particularly in France, Germany and Italy - have asked if it might not be better for the war to end, even if it came at the cost of Ukraine having to cede territory. A recent cross-Europe opinion poll suggested some voters put solving the cost-of-living crisis ahead of punishing Russia.

Others argue about the need to salvage some kind of relationship with Russia in the future.

Countries like the UK, Poland and the three Baltic States have been resisting these arguments, saying that any peace deal with Moscow that is not on Ukraine's terms would lead to further Russian aggression in the future. President Zelensky is likely to reinforce this argument when he addresses the summit virtually on Monday.

So the G7 leaders are expected to try to use the summit to clear these muddy waters, promising more weapons to Ukraine and more sanctions against Russia. The idea will be to send a signal to Russian President Vladimir Putin that the West has the strategic patience to maintain its support for Ukraine, even if it faces domestic political pressure at home from voters concerned about rising prices.

The problem for G7 leaders is they also face growing pressure to show they are tackling the global economic crisis. The soaring price of fuel and food is causing hunger and unrest across the world. And some countries are pointing the finger at the West.

Many countries in the global south do not share Western concerns about Russian aggression. They see the conflict as a European war and seem unmoved by Western arguments that Vladimir Putin is acting as a colonial aggressor. And they blame Western sanctions - as much as Russia's invasion - for the rising costs of gas and oil, and the massive shortage of wheat and fertiliser.

To try to resist this narrative, G7 countries are expected to use the summit to show they are acting to help countries round the world - with development aid, debt restructuring, climate finance, help finding alternative sources of energy and, of course, fresh efforts to get grain out of Ukraine's ports. That is why German has invited the leaders of India, Indonesia, Senegal, Argentina and South Africa to the summit, to hear their perspective and show the rest of the world the G7 is listening.

So on the one hand, these Western leaders must show resolve to keep backing Ukraine, and on the other, they must show a readiness to fix the global economic shocks that some blame, in part, on the war.

One senior US official described the dilemma thus: "How do we maximise pain on Putin's regime? How do we minimise spillbacks back to the rest of the world?"

That is quite a circle to square.