The present paper deals with the study of semilinear and non-homogeneous Schrödinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and for p ∈ (2, 2∗) with respect to non-homogeneous term g(x) ∈ L2n/2(B), which helps to find multiple solutions of our problem. More precisely, we prove the existence of two solutions to the problem 1.1 with negative and positive energy in cone Sobolev space H2,01,n/2 (B). Finally, we consider p = 2 and we prove the existence and uniqueness of Fuchsian-Poisson problem
