Bakim, SumeyyeGoldstein, Gisele RuizGoldstein, Jerome A.Kombe, Ismail2021-01-252021-01-2520200893-4983https://hdl.handle.net/11467/4469kombe, ismail/0000-0002-7217-1023WOS:000572161900004In the present paper, we first study the nonexistence of positive solutions of the following nonlinear parabolic problem {partial derivative u/partial derivative t = Delta g(u(m)) + V(x)u(m) + lambda u(q) in Omega x (0, T), u(x, 0) = u(0)(x) >= 0 in Omega, u(x, t) = 0 on partial derivative Omega x (0, T). Here, Omega is a bounded domain with smooth boundary in a complete non-compact Riemannian manifold M, 0 < m < 1, V is an element of L-loc(1)(Omega), q > 0 and A E R. Next, we prove some Hardy and Leray type inequalities with remainders on a Riemannian Manifold M. Furthermore, we obtain explicit (sometimes optimal) constants for these inequalities and present several nonexistence results with help of Hardy and Leray type inequalities on the hyperbolic space H-n.eninfo:eu-repo/semantics/closedAccessArticle3309.Oct507526Q2WOS:000572161900004Q22-s2.0-85091502113