Existence, Nagumo-Type Uniqueness and Stability of Minkowski-Curvature on Unbounded Domains

In this paper, we show the existence, uniqueness and stability of nontrivial solutions to the following Minkowski-curvature problems on unbounded domains: align* (x'√1-x²)'=f(t,\ x), t≥ t₀, limt→∞x(t)=ψ₀, limt→∞x'(t)eᵗ=0, align* where f:\ [t₀, ∞ )× R→ R is continuous, t₀>0 and ψ ₀∈ R are some given constants. Moreover, this unique solution is obtained as the uniform limit of the sequence of successive approximations.