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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. \textbf{87} (1982/83), 87 (): 131.
|
[2] |
C. Bereanu, P. Jebelean, and P. Torres, Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space,, J. Funct. Anal. \textbf{264} (2013), 264 (2013), 270.
|
[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. \textbf{265} (2013), 265 (2013), 644.
|
[4] |
H. Brezis and J. Mawhin, Periodic solutions of the forced relativistic pendulum,, Differential Integral Equations \textbf{23} (2010), 23 (2010), 801.
|
[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. \textbf{12} (2012), 12 (2012), 621.
|
[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), (2013). Google Scholar |
[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. \textbf{405} (2013) 227-239., 405 (2013), 227.
|
[8] |
C. Gerhardt, $H$-surfaces in Lorentzian manifolds,, Comm. Math. Phys. \textbf{89} (1983), 89 (1983), 523.
|
[9] |
J. Mawhin, Radial solutions of Neumann problem for periodic perturbations of the mean extrinsic curvature operator,, Milan J. Math. \textbf{79} (2011), 79 (2011), 95.
|
[10] |
P. Omari and F. Zanolin, Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential,, Comm. Partial Differential Equations {\bf 21} (1996), 21 (1996), 721.
|
show all references
References:
[1] |
R. Bartnik and L. Simon, Spacelike hypersurfaces with prescribed boundary values and mean curvature,, Comm. Math. Phys. \textbf{87} (1982/83), 87 (): 131.
|
[2] |
C. Bereanu, P. Jebelean, and P. Torres, Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space,, J. Funct. Anal. \textbf{264} (2013), 264 (2013), 270.
|
[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. \textbf{265} (2013), 265 (2013), 644.
|
[4] |
H. Brezis and J. Mawhin, Periodic solutions of the forced relativistic pendulum,, Differential Integral Equations \textbf{23} (2010), 23 (2010), 801.
|
[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. \textbf{12} (2012), 12 (2012), 621.
|
[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), (2013). Google Scholar |
[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. \textbf{405} (2013) 227-239., 405 (2013), 227.
|
[8] |
C. Gerhardt, $H$-surfaces in Lorentzian manifolds,, Comm. Math. Phys. \textbf{89} (1983), 89 (1983), 523.
|
[9] |
J. Mawhin, Radial solutions of Neumann problem for periodic perturbations of the mean extrinsic curvature operator,, Milan J. Math. \textbf{79} (2011), 79 (2011), 95.
|
[10] |
P. Omari and F. Zanolin, Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential,, Comm. Partial Differential Equations {\bf 21} (1996), 21 (1996), 721.
|
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