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We consider, in five dimensions, the effective action from heterotic stringwhich includes quantum gravity corrections up to (a')^2. The expansion, in thestring frame, is in terms of |a'R|, where R is the scalar curvature and usesthe third order Euler density, next to the Gauss-Bonnet term. For a positivetension brane and infinite extra dimension, the logarithmic class of solutionsis less dependent from fine-tuning problems than in previous formulations. Moreimportantly, the model suggests that in the full non-perturbative formulation,the string scale can be much lower than the effective Planck mass, without thestring coupling to be vanishingly small. Also a less severe fine-tuning of thebrane tension in needed.Comment: 19 pages, 5 figures LaTeX. Accepted for publication in IJMP

DILATON BRANE COSMOLOGY WITH SECOND ORDER STRING CORRECTIONS AND THE COSMOLOGICAL CONSTANT