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On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space
1. | Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Via A. Valerio 12/1, 34127 Trieste, Italy, Italy |
References:
[1] |
R. Bartnik and L. Simon, Spacelike hypersurfaces with prescribed boundary values and mean curvature, Comm. Math. Phys. 87 (1982/83), 131-152. |
[2] |
C. Bereanu, P. Jebelean, and P. Torres, Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space, J. Funct. Anal. 264 (2013), 270-287. |
[3] |
C. Bereanu, P. Jebelean, and P. Torres, Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space, J. Funct. Anal. 265 (2013), 644-659. |
[4] |
H. Brezis and J. Mawhin, Periodic solutions of the forced relativistic pendulum, Differential Integral Equations 23 (2010), 801-810. |
[5] |
I. Coelho, C. Corsato, F. Obersnel, and P. Omari, Positive solutions of the Dirichlet problem for the one-dimensional Minkowski-curvature equation, Adv. Nonlinear Stud. 12 (2012), 621-638. |
[6] |
I. Coelho, C. Corsato, and S. Rivetti, Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball, Topol. Methods Nonlinear Anal. (2013), in press. Available at: http://www.dmi.units.it/pubblicazioni/Quaderni_Matematici/624_2012.pdf |
[7] |
C. Corsato, F. Obersnel, P. Omari, and S. Rivetti, Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space, J. Math. Anal. Appl. 405 (2013) 227-239. |
[8] |
C. Gerhardt, $H$-surfaces in Lorentzian manifolds, Comm. Math. Phys. 89 (1983), 523-553. |
[9] |
J. Mawhin, Radial solutions of Neumann problem for periodic perturbations of the mean extrinsic curvature operator, Milan J. Math. 79 (2011), 95-112. |
[10] |
P. Omari and F. Zanolin, Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential, Comm. Partial Differential Equations 21 (1996), 721-733. |
show all references
References:
[1] |
R. Bartnik and L. Simon, Spacelike hypersurfaces with prescribed boundary values and mean curvature, Comm. Math. Phys. 87 (1982/83), 131-152. |
[2] |
C. Bereanu, P. Jebelean, and P. Torres, Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space, J. Funct. Anal. 264 (2013), 270-287. |
[3] |
C. Bereanu, P. Jebelean, and P. Torres, Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space, J. Funct. Anal. 265 (2013), 644-659. |
[4] |
H. Brezis and J. Mawhin, Periodic solutions of the forced relativistic pendulum, Differential Integral Equations 23 (2010), 801-810. |
[5] |
I. Coelho, C. Corsato, F. Obersnel, and P. Omari, Positive solutions of the Dirichlet problem for the one-dimensional Minkowski-curvature equation, Adv. Nonlinear Stud. 12 (2012), 621-638. |
[6] |
I. Coelho, C. Corsato, and S. Rivetti, Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball, Topol. Methods Nonlinear Anal. (2013), in press. Available at: http://www.dmi.units.it/pubblicazioni/Quaderni_Matematici/624_2012.pdf |
[7] |
C. Corsato, F. Obersnel, P. Omari, and S. Rivetti, Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space, J. Math. Anal. Appl. 405 (2013) 227-239. |
[8] |
C. Gerhardt, $H$-surfaces in Lorentzian manifolds, Comm. Math. Phys. 89 (1983), 523-553. |
[9] |
J. Mawhin, Radial solutions of Neumann problem for periodic perturbations of the mean extrinsic curvature operator, Milan J. Math. 79 (2011), 95-112. |
[10] |
P. Omari and F. Zanolin, Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential, Comm. Partial Differential Equations 21 (1996), 721-733. |
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