## 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.

### MSC:

 34L05 General spectral theory of ordinary differential operators 34B24 Sturm-Liouville theory 34B15 Nonlinear boundary value problems for ordinary differential equations
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### References:

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