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EXISTENCE, NAGUMO-TYPE UNIQUENESS AND STABILITY OF MINKOWSKI-CURVATURE ON UNBOUNDED DOMAINS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 121 / Issue 3 / December 2026
- Published online by Cambridge University Press:
- 20 April 2026, pp. 336-356
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- Article
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In this paper, we show the existence, uniqueness and stability of nontrivial solutions to the following Minkowski-curvature problems on unbounded domains:
$$ \begin{align*} \bigg(\frac{x'}{\sqrt{1-x^{\prime2}}}\bigg)'=f(t,\ x),\quad t\geq t_0, \quad \lim_{t\to\infty}x(t)=\psi_0,\quad \lim_{t\to\infty}x'(t)e^{t}=0, \end{align*} $$where $f:\ [t_0, \infty )\times \mathbb {R}\rightarrow \mathbb {R}$
is continuous, $t_0>0$
and $\psi _0\in \mathbb {R}$
are some given constants. Moreover, this unique solution is obtained as the uniform limit of the sequence of successive approximations.
