Multiple solutions for a class of nonhomogeneous semilinear equations with critical cone Sobolev exponent

In this paper, we deal with the study of a class of semilinear and nonhomogeneous Schrödinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and the critical cone Sobolev exponent with respect to the nonhomogeneous term g(x)∈L2n2(B).g(x)\in L^{\frac {n}{2}}_{2}(\mathbb {B}). Our approach improves on and generalizes the previous results in [Indian J. Pure Appl. Math. 48 (2017), pp. 133–146] and [Ann. Global Anal. Geom. 39 (2011), pp. 27–43].