MULTIPLE SOLUTIONS FOR A SINGULAR NONHOMOGENOUS BIHARMONIC EQUATION IN HEISENBERG GROUP

In this paper, we study a singular nonhomogenous biharmonic problem with Dirichlet boundary condition in Heisenberg group { delta(2)(H1)u = f(xi,u)/rho(xi)beta + is an element of h(xi) in omega u = eth u/ eth v = 0, on eth omega where omega C H-1 is a bounded smooth domain, delta(2)(H1)u = delta(2)(H1) delta(H1)u (denotes the biharmonic operator in Heisenberg group H-1 = C x R, 0 <= beta < 4 with 4 is the homogeneous dimension of H-1 and f : omega x R -> R is a continuous function which satisfies subcritical and critical exponential growth condition, h(xi) E (D-0(2),2 (omega))*, h(xi) >= 0 and h(xi) (sic) 0, rho(xi) = (|z|(4) + t(2))(1/4), xi = (z,t) is an element of H-1 with z = (x, y) is an element of R-2, is an element of is a small positive parameter. We obtain the existence and multiplicity of solutions by the Ekeland variational principle, mountain pass theorem and singular Adams inequality in Heisenberg group.