Precup, RaduRodríguez López, Jorge2020-04-062020-04-062019PrecupR. and Rodríguez-LópezJ. (2019) “Positive solutions for phi-Laplace equations with discontinuous state-dependent forcing terms”, Nonlinear Analysis: Modelling and Control, 24(3), 447-461. doi: 10.15388/NA.2019.3.8.1392-5113http://hdl.handle.net/10347/21169This paper concerns the existence, localization and multiplicity of positive solutions for a -Laplacian problem with a perturbed term that may have discontinuities in the state variable. First, the initial discontinuous differential equation is replaced by a differential inclusion with an upper semicontinuous term. Next, the existence and localization of a positive solution of the inclusion is obtained via a compression-expansion fixed point theorem for a composition of two multivalued maps, and finally, a suitable control of discontinuities allows to prove that any solution of the inclusion is a solution in the sense of Carathéodory of the initial discontinuous equation. No monotonicity assumptions on the nonlinearity are requiredeng© 2019 Vilnius University. This work is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/)https://creativecommons.org/licenses/by/4.0/Discontinuous differential equationφ-Laplacian problemPositive solutionFixed pointMultivalued mapInfinitely many solutionsjournal article10.15388/NA.2019.3.82335-8963 open access