(Non)-singular brane-world cosmology induced by quantum effects in five-dimensional dilatonic gravity

5D dilatonic gravity (bosonic sector of gauged supergravity) with a nontrivial bulk potential and with surface terms (boundary cosmological constant and trace anomaly induced effective action for brane quantum matter) is considered. For a constant bulk potential and maximally SUSY Yang-Mills theory (CFT residing on the brane) the inflationary brane world is constructed. The bulk is singular asymptotically AdS space with a nonconstant dilaton and a dilatonic de Sitter or hyperbolic brane is induced by quantum matter effects. At the same time, the dilaton on the brane is determined dynamically. All this is a natural realization of warped compactification in the AdS/CFT correspondence. For a fine-tuned toy example of a nonconstant bulk potential we find the nonsingular dilatonic brane world where the bulk again represents asymptotically AdS space and a de Sitter brane (inflationary phase of the observable Universe) is induced exclusively by quantum effects. The radii of the brane and dilaton are determined dynamically. The analytically solvable example of the exponential bulk potential leading to a singular asymptotically AdS dilatonic bulk space with a de Sitter (or hyperbolic) brane is also presented. In all cases under discussion the gravity on the brane is trapped via the Randall-Sundrum scenario. It is shown that qualitatively the same types of brane worlds occur when quantum brane matter is described by N dilaton coupled spinors.