We present the AGILE gamma-ray observations of the field containing the puzzling gamma-ray source 3EG J1835+5918. This source is one of the most remarkable unidentified EGRET sources. An unprecedentedly long AGILE monitoring of this source yields important information on the positional error box, flux evolution, and spectrum. 3EG J1835+5918 has been in the AGILE field of view several times in 2007 and 2008 for a total observing time of 138 days from 2007 Sept 04 to 2008 June 30 encompassing several weeks of continuous coverage. With an exposure time approximately twice that of EGRET, AGILE confirms the existence of a prominent gamma-ray source (AGL J1836+5926) at a position consistent with that of EGRET, although with a remarkably lower average flux value for photon energies greater than 100 MeV. A 5-day bin temporal analysis of the whole data set of AGL J1836+5926 shows some evidence for variability of the gamma-ray flux. The source spectrum between 100 MeV and 1 GeV can be fitted with a power law with photon index in the range 1.6-1.7, fully consistent with the EGRET value. The faint X-ray source RX J1836.2+5925 that has been proposed as a possible counterpart of 3EG J1835+5918 is well within the AGILE error box. Future continuous monitoring (both by AGILE and GLAST) is needed to confirm the gamma-ray flux variability and to unveil the source origin, a subject that is currently being pursued through a multiwavelength search for counterparts.
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