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.


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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