A symmetric solution of a multipoint boundary value problem at resonance. (2006) - Kosmatov, Nickolai
Abstract : We apply a coincidence degree theorem of Mawhin to show the existence of at least one symmetric solution of the nonlinear second-order multipoint boundary value problem u ″ ( t ) = f ( t, u ( t ), | u ′ ( t ) | ), t ∈ ( 0, 1 ), u ( 0 ) = ∑ i = 1 n μ i u ( ξ i ), u ( 1 − t ) = u ( t ), t ∈ [ 0, 1 ], where 0 < ξ 1 < ξ 2 < … < ξ n ≤ 1 / 2, ∑ i = 1 n μ i = 1, f : [ 0, 1 ] × ℝ 2 → ℝ with f ( t, x, y ) = f ( 1 − t, x, y ), ( t, x, y ) ∈ [ 0, 1 ] × ℝ 2, satisfying the Carathéodory conditions.