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

Summary: Values of λ are determined for which there exist positive solutions to the second-order differential equation on a measure chain,

u ΔΔ (t)+λa(t)f(u(σ(t)))=0,t[0,1],

satisfying either the conjugate boundary conditions u(0)=u(σ(1))=0 or the right focal boundary conditions u(0)=u Δ (σ(1))=0, where a and f are positive valued, and both lim x0 + f(x) x and lim x f(x) x exist.

34L05General spectral theory for OD operators
34B24Sturm-Liouville theory
34B15Nonlinear boundary value problems for ODE