### Multiplicity of solutions for an elliptic problem involving GJMS

#### Abstract

Given a compact Riemannian manifold (M, g) of dimension

n ≥ 3 without boundary, using the variational method, we study the

existence of solutions for the elliptic equation

Pk

g u = f|u|N−2u + λh|u|q−2u, (0.1)

where Pk

g is the GJMS operator of order 2k < n, h, f ∈ C∞(M), 1 <

q < 2, λ > 0 and N is the critical Sobolev exponent for the space

H2

k(M). We apply Ljusternik-Schnirelmann theory on C1-manifolds to

prove that under some conditions, the equation (0.1) admits infinitely

many solutions.

n ≥ 3 without boundary, using the variational method, we study the

existence of solutions for the elliptic equation

Pk

g u = f|u|N−2u + λh|u|q−2u, (0.1)

where Pk

g is the GJMS operator of order 2k < n, h, f ∈ C∞(M), 1 <

q < 2, λ > 0 and N is the critical Sobolev exponent for the space

H2

k(M). We apply Ljusternik-Schnirelmann theory on C1-manifolds to

prove that under some conditions, the equation (0.1) admits infinitely

many solutions.

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