ϕ−Laplacian second-order boundary value problems with parameters

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Abstract

This paper deals with a second-order fully differential equation involving a ϕ−Laplacian operator, which generalizes the more common p-Laplacian, with a parameter, applied to a nonlinearity depending on the unknown function and its first derivative. The main result states the problem’s solvability for parameter values for which there are lower and upper solutions for the problem. Singular ϕ−Laplacians considered with an application to the special relativity field.

Keywords

lower and upper solutions / Nagumo condition / regular and singular ϕ−Laplacian equations / fixed-point theory

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