Results and Estimates on Multiple Solutions of Lidstone Boundary Value Problems

We consider the following boundary value problem (-1)ny(2n)=F(t,y), n≥ 1, t ∈ (0,1), y(2i)(0)=y(2i)(1)=0, 0≧i≧n-1. Criteria are developed for the existence of two and three positive solutions of the boundary value problem. In addition, for special cases we establish upper and lower bounds for these positive solutions. Several examples are also included to dwell upon the importance of the results obtained.

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