@article{freedman_rodriguez_2020, title={ON WEAKLY NONLINEAR BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS}, volume={12}, ISBN={1848-9605}, DOI={10.7153/dea-202-12-12}, number={2}, journal={DIFFERENTIAL EQUATIONS & APPLICATIONS}, author={Freedman, Benjamin and Rodriguez, Jesus}, year={2020}, month={May}, pages={185–200} }
 @article{freedman_rodriguez_2019, title={EXISTENCE OF SOLUTIONS TO NONLINEAR LEGENDRE BOUNDARY VALUE PROBLEMS}, volume={11}, ISSN={["1848-9605"]}, DOI={10.7153/dea-2019-11-24}, abstractNote={In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a qualitative description of solutions depending on a parameter. The results presented depend on the size and limiting behavior of the nonlinearities.}, number={4}, journal={DIFFERENTIAL EQUATIONS & APPLICATIONS}, author={Freedman, Benjamin and Rodriguez, Jesus}, year={2019}, month={Nov}, pages={495–508} }
 @article{freedman_rodriguez_2019, title={On nonlinear boundary value problems in the discrete setting}, volume={25}, ISSN={["1563-5120"]}, DOI={10.1080/10236198.2019.1641497}, abstractNote={ABSTRACT Results appearing in this paper can be used to establish the solvability of nonlinear discrete time systems subject to generalized nonlinear boundary conditions. Two separate sets of results are established, each of which can be used to establish existence of solutions to problems for which previous related work proves inconclusive. The first set of results imposes conditions on the sizes of nonlinearities, while the second framework requires geometric properties of the nonlinearity in the dynamics.}, number={7}, journal={JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS}, author={Freedman, Benjamin and Rodriguez, Jesus}, year={2019}, month={Jul}, pages={994–1006} }
 @article{caldwell_freedman_settles_thomas_camacho_wirkus_2019, title={The Vicodin abuse problem: A mathematical approach}, volume={483}, ISSN={["1095-8541"]}, DOI={10.1016/j.jtbi.2019.110003}, abstractNote={The prescription drug epidemic in the United States has gained attention in recent years. Vicodin, along with its generic version, is the country's mostly widely prescribed pain reliever, and it contains a narcotic component that can lead to physical and chemical dependency. The majority of Vicodin abusers were first introduced via prescription, unlike other drugs which are often experienced for the first time due to experimentation. Most abusers report obtaining their supply from a prescription, either their own or someone else's. Although the problem with prescription drug abuse is well known, there is no standard method of addressing the problem. To better understand how to do this, we develop and analyze a mathematical model of Vicodin use and abuse, considering only those patients who were initially prescribed the drug. Through global sensitivity analysis, we show that focusing efforts on abuse prevention rather than treatment has greater success at reducing the population of Vicodin abusers. Our results demonstrate that relying solely on rehabilitation and other treatment programs is not enough to combat the prescription drug problem in the United States. We anticipate that implementing preventative measures in both prescribers and patients will reduce the number of Vicodin abusers.}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Caldwell, Wendy K. and Freedman, Benjamin and Settles, Luke and Thomas, Michael M. and Camacho, Erika T. and Wirkus, Stephen}, year={2019}, month={Dec} }
 @article{freedman_rodriguez_2018, title={ON THE SOLVABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS SUBJECT TO GENERALIZED BOUNDARY CONDITIONS}, volume={10}, ISSN={["1848-9605"]}, DOI={10.7153/dea-2018-10-22}, abstractNote={In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability of a large number of nonlinear scalar boundary value problems. We begin by giving our general strategy which involves the reformulation of our boundary value problem as an operator equation. We then proceed to establish our results and compare them to closely related previous work.}, number={3}, journal={DIFFERENTIAL EQUATIONS & APPLICATIONS}, author={Freedman, Benjamin and Rodriguez, Jesus}, year={2018}, month={Aug}, pages={317–327} }