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Zbl 1074.34079
Hao, Zhao-Cai; Debnath, Lokenath
On eigenvalue intervals and eigenfunctions of fourth-order singular boundary value problems.
(English)
[J] Appl. Math. Lett. 18, No. 5, 543-553 (2005). ISSN 0893-9659

Summary: Values of $\lambda$ are determined for which there exist positive solutions of the fourth-order singular boundary value problems $$x^{(4)}(t)=\lambda f(t, x(t)),\quad t\in (0,1),\quad x(0)= x(1)= 0,\quad x''(0)= x''(1)= 0,$$ where $f\in C((0, 1)\times (0,\infty), [0,\infty))$ and $\lambda> 0$ is a parameter. For $\lambda= 1$, we give criteria for the existence of eigenfunctions.
MSC 2000:
*34L15 Estimation of eigenvalues for OD operators
34B15 Nonlinear boundary value problems of ODE
34B18 Positive solutions of nonlinear boundary value problems
34B16 Singular nonlinear boundary value problems

Keywords: Nonlinear differential equations; Singular boundary problem; Positive solutions; Eigenvalue; Eigenfunctions

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