Multiplicity of positive solutions for a class of nonhomogeneous elliptic equations in the hyperbolic space

The paper is concerned with positive solutions to problems of the type \ -₁^₍ u - u = a (x) |u|^p-1\;u + f in B^N, u H^1 (B^{N) }, \ where BN denotes the hyperbolic space, 1 0. Subsequently, we establish the existence of two positive solutions for a (x) 1 and prove asymptotic estimates for positive solutions using barrier-type arguments. The proofs for existence combine variational arguments, key energy estimates involving hyperbolic bubbles.