Eigenvalue characterization for a class of boundary value problems

C. J. Chyan, Tamkang University, Taipei, Taiwan
J. Henderson, Baylor University, Waco, Texas, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 12. (1999), pp. 1-13.

Abstract: We consider the $n$'th order ordinary differential equation $(-1)^{n-k} y^{(n)}=\lambda a(t) f(y)$, $t\in[0,1]$, $n\geq 3$ together with the boundary condition $y^{(i)}(0)=0$, $0\leq i\leq k-1$ and $y^{(l)}=0$, $j\leq l\leq j+n-k-1$, for $1\leq j\leq k-1$ fixed. Values of $\lambda$ are characterized so that the boundary value problem has a positive solution.

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