Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem

The existence results of positive solutions are obtained for the fourth‐order periodic boundary value problem u (4) − β u ′′ + α u = f ( t , u , u ′′ ), 0 ≤ t ≤ 1, u ( i ) (0) = u ( i ) (1), i = 0, 1, 2, 3, where f : [0, 1] × ℝ + × ℝ → ℝ + is continuous, α , β ∈ ℝ, and satisfy , β > −2 π 2 , ( α / π 4 ) + ( β / π 2 ) + 1 > 0. The discussion is based on the fixed point index theory in cones.

Abstract licence: CC BY

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