Multiple solutions for a degenerate elliptic equation involving sublinear terms at infinity

Some multiplicity results are presented for the eigenvalue problem( P λ , μ ) { − div ( | x | − 2 a ∇ u ) = λ | x | − 2 b f ( u ) + μ | x | − 2 c g ( u ) in Ω , u = 0 on ∂ Ω , where Ω ⊂ R n ( n ⩾ 3 ) is an open bounded domain with smooth boundary, 0 ∈ Ω , 0 < a < n − 2 2 , a ⩽ b , c < a + 1 , and f : R → R is sublinear at infinity and superlinear at the origin. Various cases are treated depending on the behaviour of the nonlinear term g.