Eigenvalues of Lidstone boundary value problems

We consider the following boundary value problem: (-1)^ny^(^2^n^)=@lF(t,y),n>=1,t@?(0,1),y^(^2^i^)(0)=y^(^2^i^)(1)=0,0=0. The values of @l are characterized so that the boundary value problem has a positive solution. In addition, we derive explicit intervals of @l such that for any @l in the interval, existence of a positive solution of the boundary value problem is guaranteed. Several examples are also included to dwell upon the importance of the results obtained.

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