Positive Solutions for Asymptotically Linear Cone-Degenerate Elliptic Equations

In this paper, the authors study the asymptotically linear elliptic equation on manifold with conical singularities -Delta(B)u + lambda u = a(z)f(u), u >= 0 in R-+(N), where N = n + 1 >= 3, lambda > 0, z = (t, x(1), ..., x(n)), and Delta(B) = (t partial derivative(t))(2) + partial derivative(2)(x1) + ... + partial derivative(2)(xn). Combining properties of cone-degenerate operator, the Pohozaev manifold and qualitative properties of the ground state solution for the limit equation, we obtain a positive solution under some suitable conditions on a and f.