Bifurcation and Calabi-Bernstein type asymptotic property of solutions for the one-dimensional Minkowski-curvature equation

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.