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arXiv · 2608.05711

Positive Solutions for a One-Dimensional Minkowski-Curvature Equation with a Sign-Changing Nonlinearity under Mixed Boundary Conditions

Ao Xiao
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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.

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Ao Xiao. 2026-08-06. Positive Solutions for a One-Dimensional Minkowski-Curvature Equation with a Sign-Changing Nonlinearity under Mixed Boundary Conditions. https://arxiv.org/abs/2608.05711

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