Figueroa Sestelo, RubénGrossinho, Maria do Rosário2020-04-272020-04-272015Figueroa, R., Grossinho, M.d.R. On some nonlinear boundary value problems related to a Black-Scholes model with transaction costs. Bound Value Probl 2015, 145 (2015). https://doi.org/10.1186/s13661-015-0410-91687-2770http://hdl.handle.net/10347/21774We deal with some generalizations on a Black-Scholes model arising in financial mathematics. As a novelty in this paper, we consider a variable volatility and abstract functional boundary conditions, which allow us to treat a very large class of problems involving Black-Scholes equation. Our main results involve the existence of extremal solutions in presence of lower and upper solutions. Some examples of applications are provided too.eng© 2015 Figueroa and Grossinho. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were madehttp://creativecommons.org/licenses/by/4.0/Black-Scholes equationFunctional conditionsDiscontinuous ODE’sjournal article10.1186/s13661-015-0410-9open access