Eigenvalue conditions and positive solutions. (English) Zbl 0949.34015

Summary: The authors are concerned with proving the existence of positive solutions to general two-point boundary value problems for the nonlinear equation \[ Lx(t):= -[r(t) x^\Delta(t)]^\Delta+ q(t) x^\sigma(t)= f(t, x^\sigma(t)). \] Here, the independent variable \(t\) is in a “measure chain”. They use fixed point theorems for operators on a Banach space.


34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34L05 General spectral theory of ordinary differential operators
39A10 Additive difference equations
34B24 Sturm-Liouville theory
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