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We study gravity interacting with a special kind of QCD-inspired nonlineargauge field system which earlier was shown to yield confinement-type effectivepotential (the "Cornell potential") between charged fermions ("quarks") in flatspace-time. We find new static spherically symmetric solutions generalizing theusual Reissner-Nordstroem-de-Sitter and Reissner-Nordstroem-anti-de-Sitterblack holes with the following additional properties: (i) appearance of aconstant radial electric field (in addition to the Coulomb one); (ii) novelmechanism of {\em dynamical generation} of cosmological constant through thenon-Maxwell gauge field dynamics; (iii) appearance of confining-type effectivepotential in charged test particle dynamics in the above black holebackgrounds.

Asymptotically de Sitter and anti-de Sitter Black Holes with Confining Electric Potential