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Eigenvalue problems for nonlinear differential equations on a measure chain. (English) Zbl 0953.34068
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.

34L05General spectral theory for OD operators
34B24Sturm-Liouville theory
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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