Multiple Positive Solutions for nth Order Multipoint Boundary Value Problem. (20th June 2010) - Li, Yaohong; Wei, Zhongli
Abstract : We study the existence of multiple positive solutions forn th-order multipoint boundary value problem.u ( n ) ( t ) + a ( t ) f ( u ( t ) ) = 0, t ∈ ( 0, 1 ), u ( j - 1 ) ( 0 ) = 0 ( j = 1, 2, …, n - 1 ), u ( 1 ) = ∑ i = 1 m α i u ( η i ), wheren ≥ 2, 0 < η 1 < η 2 < ⋯ < η m < 1, α i > 0, i = 1, 2, …, m . We obtained the existence of multiple positive solutions by applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed-point theorem. The results obtained in this paper are different from those in the literature.