The phrase "a backdrop of declining" is correct and usable in written English.
It can be used to describe a situation or context where there is a decrease or deterioration in a particular aspect, often in relation to events or trends.
Example: "The company made strategic changes against a backdrop of declining sales and increasing competition."
Alternatives: "a context of decreasing" or "a setting of diminishing".
But it did so hesitantly, against a backdrop of declining domestic interest in foreign affairs (a decline shared in Europe).
This is against a backdrop of declining numbers of asylum applications across Europe over the past decade – in particular, UNHCR report a drop of 33% in applications in southern EU member states between 2009 and 2010.
The management change comes amid a backdrop of declining assets at Schroder, including a net decrease of £3 billion ($4.7 billion) last year in funds that Schroder manages for American institutional investors.
Even against a backdrop of declining album sales across the entire music industry (neither One Direction album has broken the 5m worldwide sales barrier, for instance) these figures would not exactly make for a great Powerpoint presentation.
And this comes under the heading of "trust and perception": The energy sector in the UK is currently the subject of unprecedented public and political debate and scrutiny against a backdrop of declining disposable income for many customers.
Of course, this is also playing out against a backdrop of declining spending and rising delinquencies.
The European Union Railway Packages, a strategy for the revitalization of the railways in Europe, against a backdrop of decline, separated of infrastructure and operations and opened rail markets to competition.
In Germany, state spending on research and education has increased by 20% since 2010, against an overall backdrop of declining public spending.
Managing director Paul Warwick said: "Our industry is operating in a mature environment, against a backdrop of a declining oil price and ever-increasing operating costs alongside falling production levels, reduction in exploration and asset integrity and maintenance issues.
This week, at the Olympus Fashion Week in New York, top American designers presented their Fall 2005 collections against a backdrop of a declining dollar and tumult at many of Europe's largest fashion houses.
Talisman Sinopec managing director Paul Warwick said: "Our industry is operating in a mature environment, against a backdrop of a declining oil price and ever-increasing operating costs alongside falling production levels, reduction in exploration and asset integrity and maintenance issues.
