Eigenvalues of boundary value problems for higher order differential equations

Abstract

We shall consider the boundary value problem y(n) + λQ(t, y, y′, y(n-2)) = λP (t, y, y′, y (n-1)), n ≥ 2, t E(0,1), y(i) (0) = 0, 0 ≤ i ≤ n-3, αy(n-2) (0) β-y (n-1) (0) = 0, βy(n-2)(1) +δy(n-1) = 0, where λ>0,α,β,γ and are constants satisfying α γ+αδ +βγ> 0,β,δ ≥ 0,β +α 0 and δ +γ> 0 to characterize the values of λso that it has a positive solution. For the special case λ = 1, sufficient conditions are also established for the existence of positive solutions. © 1996 OPA.