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Zbl 0953.34068
Chyan, Chuan Jen; Henderson, Johnny
Eigenvalue problems for nonlinear differential equations on a measure chain. (English)
[J] J. Math. Anal. Appl. 245, No.2, 547-559 (2000). ISSN 0022-247X

Summary: Values of $\lambda$ are determined for which there exist positive solutions to the second-order differential equation on a measure chain, $$u^{\Delta\Delta}(t)+\lambda a(t) f(u(\sigma(t)))= 0,\quad t\in [0,1],$$ satisfying either the conjugate boundary conditions $u(0)= u(\sigma(1))= 0$ or the right focal boundary conditions $u(0)= u^\Delta(\sigma(1))= 0$, where $a$ and $f$ are positive valued, and both $\lim_{x\to 0^+} {f(x)\over x}$ and $\lim_{x\to \infty}{f(x)\over x}$ exist.

MSC 2000:: *34L05 General spectral theory for ODE
34B24 Sturm-Liouville theory
34B15 Nonlinear boundary value problems of ODE

Keywords: positive solutions; second-order differential equation; measure chain

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