Infinitely many solutions to superlinear second order m-point boundary value problems

We consider the boundary value problem u ″ ( x ) + g ( u ( x ) ) + p ( x , u ( x ) , u ′ ( x ) ) = 0 , x ∈ ( 0 , 1 ) , u ( 0 ) = 0 , u ( 1 ) = ∑ i = 1 m - 2 α i u ( η i ) , where: (1) m ≥ 3, ηi ∈ (0, 1) and αi > 0 with A : = ∑ i = 1 m - 2 α i < 1 ; (2) g : → is continuous and satisfies g ( s ) s > 0 , s ≠ 0 , and lim s → ∞ g ( s ) s = ∞ ; (3) p : [0, 1] × 2 → is continuous and satisfies | p ( x , u , v ) | ≤ C + β | u | , x ∈ [ 0 , 1 ] ( u , v ) ∈ 2 for some C > 0 and β ∈ (0, 1/2). We obtain infinitely many solutions having specified nodal properties by the bifurcation techniques. MSC(2000). 34B15, 58E05, 47J10