Abstract 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-x^{2}) '=f (t, \ x), t t₀, ₓx (t) =₀, ₓx' (t) e^t=0, align* where f: \ [t₀, ) R R is continuous, t₀>0 and ₀ R are some given constants. Moreover, this unique solution is obtained as the uniform limit of the sequence of successive approximations.
Chen et al. (Mon,) studied this question.
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