We consider a model of high-T c superconductors with an anisotropic boson-mediated pairing mechanism corresponding to the nearest-neighbor interactions, and the one-particle dispersion relation characterized by 2D Fermi surface nesting. Based upon the tight-binding or t−J approaches with half-filling we show that the effective pairing potential coefficients and the dispersion relation, which can be characterized by the parameter η = 2t 1 /t 0 , have a diverse and mutually competing influence on the values of transition temperatures. The spin-singlet d-wave symmetry superconducting state is realized for small values of η, whereas for sufficiently large values, the spin-triplet p-wave symmetry superconducting state should be formed. The specific heat jump and the isotope shift, as functions of the parameter η, are evaluated for the d-and p-wave symmetry.