Existence and Multiplicity of Positive Solutions of a Class of Fourth-order Four-point Boundary Value Problems
In this paper,we study the existence and multiplicity of positive solutions of the fourth-order four-point boundary value problem （{）u(4)(t)-g(t)f(t,u(t),u"(t)) =0,t,∈ [0,1],u(0) =0,u(1) =0,au"(ξ1)-bu"(ξ1) =0,cu"(ξ2) +du(") (ξ2) =0,where 0≤ξ ≤ξξ2 ≤1 ;a,b,c,d are nonnegative constants,f:[0,1] × [0,+ ∞) × (-∞,0] →[0,+ ∞) is a Carathéodory function,g ∈ L1 [0,1].By using the fixed point index theory,some optimal results are obtained.
fourth-order four-point boundary value problemspositive solutionsexistenceeigenvalue criteriafixed point index
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