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where 1 0 are eigenvalue parameters. In order to describe and motivate the results of this paper, let us briefly recall some of the known results concerning two-parameter Sturm–Liouville problems. There are many works concerning linear two-parameter problems. One of the main objectives is to investigate asymptotic properties of eigenvalues. In this direction, for instance, there are works of Binding and Browne [1], Faierman [2], Turyn [6] and Weinstein and Keller [7]. We also refer to Faierman [3] and the references cited therein. In particular, Binding and Browne [1] considered the following equation:

Variational eigencurve and bifurcation for two-parameter nonlinear Sturm-Liouville equations