EXISTENCE OF SOLUTIONS FOR THE SEMILINEAR CORNER DEGENERATE ELLIPTIC EQUATIONS

In this paper, we are concerned with the following elliptic equations: {-Delta(M)u = lambda f in z := (r, x, t) is an element of M-0, u = 0 on partial derivative M. Here, lambda > 0 and M = [0, 1) x X x [0, 1) as a local model of stretched cornermanifolds, that is, the manifolds with corner singularities with dimension N = n+ 2 >= 3. Here X is a closed compact submanifold of dimension n embedded in the unit sphere of Rn+1. We study the existence of nontrivial weak solutions for the semilinear corner degenerate elliptic equations without the Ambrosetti and Rabinowitz condition via the mountain pass theorem and fountain theorem.