In this paper, the authors study the asymptotically linear elliptic equation on manifold with conical singularities
$$ - {\Delta _{\mathbb{B}}}u + \lambda u = a\left( z \right)f\left( u \right),\,\,\,\,\,\,u \ge 0\,\,{\rm{in}}\,\,_ + ^N,$$
where N = n + 1 ≥ 3, λ > 0, z = (t, x1, ⋯, xn), and
$${\Delta _{\mathbb{B}}} = {\left( {t{\partial _t}} \right)^2} + \partial _{{x_1}}^2 + \cdots + \partial _{{x_n}}^2$$
. Combining properties of cone-degenerate operator, the Pohozaev manifold and qualitative properties of the ground stat...
