Kirchhoff-type problems on a geodesic ball of the hyperbolic space

In this paper we study the existence of (weak) solutions for some Kirchhoff-type problems whose simple prototype is given by {-(a + b integral(B)vertical bar del(H)u(sigma)vertical bar(2) d mu) Delta(H)u = lambda f(u) in B-R u = 0 on partial derivative B-R, where Delta(H) denotes the Laplace-Beltrami operator on the ball model of the Hyperbolic space B-N (with N >= 3), a, b and lambda are real parameters, B-R subset of B-N is a geodesic ball centered in zero of radius R and f is a subcritical continuous function. The Kirchhoff term is allowed to vanish at the origin covering the degenerate case. The main technical approach is based on variational and topological methods. (C) 2018 Published by Elsevier Ltd.