"problem upon" is not a correct and usable phrase in written English.
You can use the phrase "upon encountering" or "upon facing" instead. For example: "Upon facing this problem, I took a step back and considered all my options."
He had problem upon problem, many self-induced.
I became involved, along with thousands of other researchers, in solving this problem upon reading a blogpost by Cambridge mathematician Tim Gowers.
With SoBig, many computer users whose machines become infected often bring the problem upon themselves by trying to open the attachment that comes with the e-mail message.
In politics there are "no lasting victories" as there are in fiction, Tiro remarks, "only the remorseless grinding forward of events", piling problem upon problem for the harassed, beleaguered Cicero.
CVS Caremark said that the subsidiary had inadvertently posted inaccurate prices for certain generic drugs on a Web site maintained by the Centers for Medicare and Medicaid Services and that the company had rectified the pricing problem upon learning of it.
Figure 4 depicts a simplified thermal problem upon which the model is built.
Greece may have brought its problems upon itself.
He is defiant when asked if he brought his political problems upon himself.
Boris Berezovsky, a Gusinsky rival, did not join the letter, saying that Mr. Gusinsky had brought his problems upon himself but should not have been jailed.
The writer could have problems upon resale if the building was being used in a way inconsistent with the certificate on file with the city.
Critics say that drugmakers bring these problems upon themselves by running lots of trials simply to collect more data for marketing later on.
