Abstract
In this paper, the nonlinear boundary value problem { − ( p ( t ) u ′ ) ′ + q ( t ) u = λ f ( t , u ) , 0 ≤ t ≤ ω , u ( 0 ) = u ( ω ) , p ( 0 ) u ′ ( 0 ) = p ( ω ) u ′ ( ω ) , is studied. By using the fixed point index theory, some existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of λ . The results obtained herein generalize and improve the main results of [J.R. Graef, L. Kong, H. Wang, Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem, J. Differential Equations 245 (2008) 1185–1197; X. Hao, L. Liu, Y. Wu, Existence and multiplicity results for nonlinear periodic boundary value problems, Nonlinear Anal. 72 (2010) 3635–3642] and some other known results.
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