Abstract
In this paper we study the existence of (weak) solutions for some Kirchhoff-type problems whose simple prototype is given by −a+b∫B|∇Hu(σ)|2dμΔHu=λf(u)inBRu=0on∂BR,where ΔH denotes the Laplace–Beltrami operator on the ball model of the Hyperbolic space BN (with N≥3), a,b and λ are real parameters, BR⊂BN 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.
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