Abstract
In this paper, we investigate the global structure of bifurcation branches of one-sign solutions and sign-changing solutions for one-dimensional Minkowski-curvature problems with a strong singular weight. Our interest of the nonlinearity is either linear or sublinear near zero. Growth conditions near ∞ are not necessary and the proofs are mainly employed by bifurcation theories based on Whyburn's limit argument and analysis techniques. We also show Calabi-Bernstein type asymptotic property of one-sign solutions by proving that one-sign solutions on two bifurcation branches converge to two linear functions.
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