Global Structure of Nodal Solutions for Second-Order m-Point Boundary Value Problems with Superlinear Nonlinearities. (28th September 2010)

• Record Type: Journal Article
• Authors: An, Yulian
• Other Names: Minhós Feliz Manuel Academic Editor.
• Is Part Of: Boundary value problems. Volume 2011(2011)
• Publication Date: 2010-09-28
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2011/715836
• Languages: English
• ISSNs: 1687-2762

Abstract

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.