Global Structure of Nodal Solutions for Second-Order m-Point Boundary Value Problems with Superlinear Nonlinearities. (28th September 2010) - An, Yulian
Abstract : We consider the nonlinear eigenvalue problemsu ″ + λ f ( u ) = 0, 0 < t < 1, u ( 0 ) = 0, u ( 1 ) = ∑ i = 1 m - 2 α i u ( η i ), wherem ≥ 3, η i ∈ ( 0, 1 ), andα i > 0 fori = 1, …, m - 2, with∑ i = 1 m - 2 α i < 1, andf ∈ C 1 ( ℝ 0 , ℝ ) ∩ C ( ℝ, ℝ ) satisfiesf ( s ) s > 0 fors ≠ 0, andf 0 = ∞, wheref 0 = lim | s | → 0 f ( s ) / s . We investigate the global structure of nodal solutions by using the Rabinowitz's global bifurcation theorem.