AI 中文总结
该研究证明了混合边界条件下带变号非线性项的一维闵可夫斯基曲率方程正解的存在性，通过不变锥、不动点指数等方法推导，还得到了可直接验证的渐近准则。
AI 中文摘要
我们建立了混合边界条件下带变号非线性项的一维闵可夫斯基曲率方程正解的存在性。非负线性平移与相关线性问题的格林核生成不变锥，主特征值比较与不动点指数给出零附近的锥扩张和无穷远处的锥压缩。全局定义的辅助方程与首次接触论证表明所得解斜率小于1，故满足原方程。我们还推导了可直接验证的渐近准则。
英文摘要
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.
Comments15 pages, no figures
