Eigenvalues of complementary Lidstone boundary value problems

AbstractWe consider the following complementary Lidstone boundary value problem (-1)my(2m+1)(t)=λF(t,y(t),y′(t)),t∈(0,1)y(0)=0,y(2k-1)(0)=y(2k-1)(1)=0,1≤k≤m where λ > 0. The values of λ are characterized so that the boundary value problem has a positive solution. Moreover, we derive explicit intervals of λ such that for any λ in the interval, the existence of a positive solution of the boundary value problem is guaranteed. Some examples are also included to illustrate the results obtained. Note that the nonlinear term F depends on y' and this derivative dependence is seldom investigated in the literature.AMS Subject Classification: 34B15.

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