Acknowledgement
This work was financially supported by a 2-Year Research Grant of Pusan National University.
References
- R. Bartnik, L. Simon, Spacelike hypersurfaces with prescribed boundary values and mean curvature, Commun. Math. Phys. 87 (1982) 131-152. https://doi.org/10.1007/BF01211061
- A.E. Treibergs, Entire spacelike hypersurfaces of constant mean curvature in Minkowski space, Invent. Math. 66 (1982) 39-56. https://doi.org/10.1007/BF01404755
- C. Gerhardt, H-surfaces in Lorentzian manifolds, Commun. Math. Phys. 89 (1983) 523-553. https://doi.org/10.1007/BF01214742
- C. Bereanu, P. Jebelean, J. Mawhin, Radial solutions for Neumann problems involving mean curvature operators in Euclidean and Minkowski spaces, Math. Nachr. 283 (2010) 379-391. https://doi.org/10.1002/mana.200910083
- C. Bereanu, P. Jebelean, J. Mawhin, Multiple solutions for Neumann and periodic problems with singular φ-Laplacian, J. Funct. Anal. 261 (2011) 3226-3246. https://doi.org/10.1016/j.jfa.2011.07.027
- C. Bereanu, P. Jebelean, J. Mawhin, Radial solutions of Neumann problems involving mean extrinsic curvature and periodic nonlinearities, Calc. Var. 46 (2013) 113-122. https://doi.org/10.1007/s00526-011-0476-x
- I. Coelho, C. Corsato, F. Obersnel, P. Omari, Positive solutions of the Dirichlet problem for one-dimensional Minkowski-curvature equation, Adv. Nonlinear Stud. 12 (2012) 621-638. https://doi.org/10.1515/ans-2012-0310
- C. Bereanu, P. Jebelean, P.J. Torres, Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space, J. Funct. Anal. 264 (2013) 270-287. https://doi.org/10.1016/j.jfa.2012.10.010
- C. Bereanu, P. Jebelean, P.J. Torres, Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space, J. Funct. Anal. 265 (2013) 644-659. https://doi.org/10.1016/j.jfa.2013.04.006
- C. Bereanu, P. Jebelean, J. Mawhin, Radial solutions for some nonlinear problems involving mean curvature operators in Euclidean and Minkowski spaces, Proc. Amer. Math. Soc. 137 (2009) 161-169. https://doi.org/10.1090/S0002-9939-08-09612-3
- R. Ma, H. Gao, Y. Lu, Global structure of radial positive solutions for a prescribed mean curvature problem in a ball, J. Funct. Anal. 270 (2016) 2430-2455. https://doi.org/10.1016/j.jfa.2016.01.020
- G. Dai, Bifurcation and positive solutions for problem with mean curvature operator in Minkowski space, Calc. Var. 55 (2016) 1-17. https://doi.org/10.1007/s00526-015-0942-y
- G. Dai, J. Wang, Nodal solutions to problem with mean curvature operator in Minkowski space, Differential and Integral Equations 30 (2017) 463-480.
- B.H. Im, E.K. Lee, Y.H. Lee, A global bifurcation phenomenon for second order singular boundary value problems, J. Math. Anal. Appl. 308 (2005) 61-78. https://doi.org/10.1016/j.jmaa.2004.10.054
- P.H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal. 7 (1971) 487-513. https://doi.org/10.1016/0022-1236(71)90030-9
- H. Asakawa, Nonresonant singular two-point boundary value problems, Nonlinear Anal. 44 (2001) 791-809. https://doi.org/10.1016/S0362-546X(99)00308-9
- R. Kajikiya, Y.H. Lee, I. Sim, One-dimensional p-Laplacian with a strong singular indefinite weight, I. Eigenvalue, J. Differential Equations 244 (2008) 1985-2019. https://doi.org/10.1016/j.jde.2007.10.030
- R. Kajikiya, Y.H. Lee, I. Sim, Bifurcation of sign-changing solutions for one-dimensional p-Laplacian with a strong singular weight; p-sublinear at ∞, Nonlinear Anal. 71 (2009) 1235-1249. https://doi.org/10.1016/j.na.2008.11.056
- R. Yang, Y.H. Lee, Bifurcation of positive radial solutions for a prescribed mean curvature problem on an exterior domain, Advances in Differential Equations 25 Number 3-4 (2020) 161-190.
- R. Yang, Y.H. Lee, and I. Sim, Bifurcation of nodal radial solutions for a prescribed mean curvature problem on an exterior domain, J. Differential Equations 268 (2020) 4464-4490. https://doi.org/10.1016/j.jde.2019.10.035
- J.K. Hunter, B. Nachtergaele, Applied Analysis, World Scientific, London 2001.
- G.T. Whyburn, Topological Analysis, Princeton University Press, Princeton, 1958.
- R. Ma, Y. An, Global structure of positive solutions for nonlocal boundary value problems involving integral conditions, Nonlinear Anal. 71 (2009) 4364-4376. https://doi.org/10.1016/j.na.2009.02.113
- H. Luo, R. Ma, The existence and application of unbounded connected components, J. Appl. Math. 2014 (2014), 7 pp.
- E.N. Dancer, On the structure of solutions of non-linear eigenvalue problems, Indiana Univ. Math. J. 23 (1974), 1069-1076. https://doi.org/10.1512/iumj.1974.23.23087
-
R. Yang, I. Sim, and Y.H. Lee,
$\frac{{\pi}}{4}$ -tangentiality of solutions for one-dimensional Minkowski-curvature problems, Advances in Nonlinear Analysis 9(1) (2020) 1463-1479. https://doi.org/10.1515/anona-2020-0061