Oscillation of a class of differential equations with generalized phi-Laplacian

The oscillation of the nonlinear differential equation (a(t)Φ(x′))′+b(t)F(x)=0, where Φ is an increasing odd homeomorphism, is considered when the weight b is not summable near infinity. We extend previous results, stated for equations with the classical p-Laplacian, by obtaining necessary and sufficient conditions of integral type for the oscillation. The role of the boundedness of Im Φ [Dom Φ] is analyzed in detail. Our results includes the case Φ^{∗}∘F linear near zero or near infinity, where Φ^{∗} is the inverse of Φ. Several examples, concerning the curvature or relativity operator, illustrate our results.