Positive solutions to semipositone problems with mean curvature operator in Minkowski space
Year: 2026
Type: preprint
Abstract: We establish the existence of a positive solution for a one-dimensional Minkowski-curvature equation with mixed boundary conditions and a sign-changing nonlinearity. A nonnegative linear shift and the Green kernel of the associated linear problem produce an invariant cone. Principal-eigenvalue comparisons and the fixed point index give cone expansion near zero and compression at infinity. A globally defined auxiliary equation and a first-contact argument show that the resulting solution has slope below one and hence solves the original equation. We also derive a directly verifiable asymptotic criterion.
Source: arXiv (Cornell University)
Author: Xiao, Ao
Institution: Northwest Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7201848137