Abstract
We consider the existence of at least one positive solution to a semipositone boundary value problem with nonlocal, nonlinear boundary conditions, which can be quite general since the nonlinearity is realized as a Stieltjes integral. By assuming that the associated Stieltjes measure decomposes in a certain way, the classical Leray-Schauder degree is utilized to derive the existence result.
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Goodrich, C.S. A note on semipositone boundary value problems with nonlocal, nonlinear boundary conditions. Arch. Math. 103, 177–187 (2014). https://doi.org/10.1007/s00013-014-0678-5
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DOI: https://doi.org/10.1007/s00013-014-0678-5