CANO-CASANOVA S, LÓPEZ-GÓMEZ J, TAKIMOTO K. A Quasilinear Parabolic Perturbation of the Linear Heat Equation[J]. Journal of Differential Equations, 2012, 252(1): 323-343. doi: 10.1016/j.jde.2011.09.018
COFFMAN C V, ZIEMER W K. A Prescribed Mean Curvature Problem on Domains without Radial Symmetry[J]. SIAM Journal on Mathematical Analysis, 1991, 22(4): 982-990. doi: 10.1137/0522063
PAN H J, XING R X. Sub- and Supersolution Methods for Prescribed Mean Curvature Equations with Dirichlet Boundary Conditions[J]. Journal of Differential Equations, 2013, 254(3): 1464-1499. doi: 10.1016/j.jde.2012.10.025
FINN R. On the Equations of Capillarity[J]. Journal of Mathematical Fluid Mechanics, 2001, 3(2): 139-151. doi: 10.1007/PL00000966
CORSATO C, DE COSTER C, OMARI P. The Dirichlet Problem for a Prescribed Anisotropic Mean Curvature Equation: Existence, Uniqueness and Regularity of Solutions[J]. Journal of Differential Equations, 2016, 260(5): 4572-4618. doi: 10.1016/j.jde.2015.11.024
BONHEURE D, HABETS P, OBERSNEL F, et al. Classical and Non-Classical Solutions of a Prescribed Curvature Equation[J]. Journal of Differential Equations, 2007, 243(2): 208-237. doi: 10.1016/j.jde.2007.05.031
HABETS P, OMARI P. Multiple Positive Solutions of a one-Dimensional Prescribed Mean Curvature Problem[J]. Communications in Contemporary Mathematics, 2007, 9(5): 701-730. doi: 10.1142/S0219199707002617
KUSAHARA T, USAMI H. A Barrier Method for Quasilinear Ordinary Differential Equations of the Curvature Type[J]. Czechoslovak Mathematical Journal, 2000, 50(1): 185-196. doi: 10.1023/A:1022409808258
PAN H J. One-Dimensional Prescribed Mean Curvature Equation with Exponential Nonlinearity[J]. Nonlinear Analysis: Theory, Methods & Applications, 2009, 70(2): 999-1010.
PAN H J, XING R X. Time Maps and Exact Multiplicity Results for One-Dimensional Prescribed Mean Curvature Equations[J]. Nonlinear Analysis: Theory, Methods & Applications, 2011, 74(4): 1234-1260.
LU Y Q, MA R Y, GAO H L. Existence and Multiplicity of Positive Solutions for One-Dimensional Prescribed Mean Curvature Equations[J]. Boundary Value Problems, 2014, 2014: 120. doi: 10.1186/1687-2770-2014-120
CORSATO C, OMARI P, ZANOLIN F. Subharmonic Solutions of the Prescribed Curvature Equation[J]. Communications in Contemporary Mathematics, 2016, 18(3): 1550042. doi: 10.1142/S021919971550042X
LÓPEZ-GÓMEZ J, OMARI P, RIVETTI S. Positive Solutions of a One-Dimensional Indefinite Capillarity-Type Problem: a Variational Approach[J]. Journal of Differential Equations, 2017, 262(3): 2335-2392. doi: 10.1016/j.jde.2016.10.046
HE Z Q, MIAO L Y. Uniqueness and Multiplicity of Positive Solutions for One-Dimensional Prescribed Mean Curvature Equation in Minkowski Space[J]. AIMS Mathematics, 2020, 5(4): 3840-3850. doi: 10.3934/math.2020249
DEIMLING K. Nonlinear Functional Analysis[M]. Berlin: Springer, 1985.
MANÁSEVICH R, MAWHIN J. Boundary Value Problems for Nonlinear Perturbations of Vector P-Laplacian-Like Operators[J]. Journal of the Korean Mathematical Society, 2000, 37: 665-685.
WANG H Y. On the Number of Positive Solutions of Nonlinear Systems[J]. Journal of Mathematical Analysis and Applications, 2003, 281(1): 287-306.