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Journal of mathematical analysis and applications, ISSN 0022-247X, 09/2013, Volume 405, Issue 1, pp. 227 - 239
We prove the existence of multiple positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space {−div(∇u/1−|∇u|2)=f(x,u,∇u)in Ω,u=0on ∂Ω. Here Ω... 
Critical point theory | Multiplicity | Positive solution | Minkowski space | Non-existence | Quasilinear elliptic equation | Dirichlet boundary condition | Mean curvature | Topological degree | Existence | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 12/2016, Volume 106, Issue 6, pp. 1122 - 1140
We are interested in providing new results on the following prescribed mean curvature equation in Lorentz–Minkowski space∇⋅[∇u1−|∇u|2... 
Quasilinear Elliptic Equations | ODEs techniques | Mean curvature operator | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Advances in nonlinear analysis, ISSN 2191-9496, 06/2018, Volume 8, Issue 1, pp. 1227 - 1234
In this paper, we consider the analogous of the Hénon equation for the prescribed mean curvature problem in , both in the Euclidean and in the Minkowski spaces... 
ODEs techniques | Quasilinear elliptic equations | mean curvature operator | 35J62 | 35J93 | 35A24 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | odes techniques | quasilinear elliptic equations | 35a24 | 35j93 | 35j62
Journal Article
Communications on pure and applied analysis, ISSN 1534-0392, 09/2012, Volume 11, Issue 5, pp. 1911 - 1922
...; by using the Second Fundamental Form we relate it to the Classical and Levi Mean Curvature... 
Characteristic direction for hypersurfaces | Quasilinear degenerate elliptic PDEs | Viscosity solutions | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
Georgian mathematical journal, ISSN 1072-947X, 03/2017, Volume 24, Issue 1, pp. 113 - 134
We discuss existence, multiplicity, localisation and stability properties of solutions of the Dirichlet problem associated with the gradient dependent prescribed mean curvature equation in the Lorentz... 
quasilinear elliptic problem | multiplicity | 35J75 | 35J62 | 35J93 | 35B35 | existence | partial differential equation | 35J25 | orderinstability | Dirichlet condition | lower and upper solutions | 47H07 | Mean curvature | order stability | Lorentz–Minkowski space | order instability | Lorentz-Minkowski space | Physical Sciences | Mathematics | Science & Technology
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 11/2019, Volume 268, Issue 10, pp. 6033 - 6066
... (which includes the m-Laplace and the m-mean curvature operator) we obtain optimal ranges of exponents p,q and α... 
m-Laplace operator | Quasilinear elliptic inequalities | Existence and nonexistence of positive solutions | m-Mean curvature operator | Physical Sciences | Mathematics | Science & Technology
Journal Article
Journal of the Australian Mathematical Society (2001), ISSN 1446-7887, 08/2016, Volume 101, Issue 1, pp. 118 - 144
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 03/2017, Volume 262, Issue 6, pp. 3759 - 3804
..., ∞-Laplace, mean curvature of graph, and even strongly degenerate operators, in addition to some nonlocal quasilinear operators appearing in the existing literature... 
Infinity-Laplace | Local limits | p-Laplace | Nonlocal quasilinear equations | Viscosity solutions | Well-posedness | Physical Sciences | Mathematics | Science & Technology | Analysis of PDEs
Journal Article
Annali di matematica pura ed applicata, ISSN 1618-1891, 10/2018, Volume 198, Issue 3, pp. 749 - 772
Journal Article
Communications in contemporary mathematics, ISSN 0219-1997, 04/2017, Volume 19, Issue 2, p. 1650006
We provide sufficient conditions for the existence of a uniparametric family of entire spacelike graphs with prescribed mean curvature in a Friedmann–Lemaître–Robertson... 
Singular f-Laplacian | Quasilinear elliptic equation | Dirichlet boundary condition | Prescribed mean curvature function | Friedmann-Lemâitre-Robertson-Walker spacetime | Entire spacelike graph | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Graphs | Dirichlet problem | Curvature
Journal Article
Monatshefte für Mathematik, ISSN 1436-5081, 11/2017, Volume 187, Issue 2, pp. 315 - 325
Journal Article
Topological methods in nonlinear analysis, ISSN 1230-3429, 09/2014, Volume 44, Issue 1, pp. 23 - 39
We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div... 
Radial solution | Variational methods | Multiplicity | Positive solution | Quasilinear elliptic differential equation | Minkowski-curvature | Dirichlet boundary condition | Existence | Physical Sciences | Mathematics | Science & Technology
Journal Article
Journal of Geometric Analysis, ISSN 1050-6926, 7/2012, Volume 22, Issue 3, pp. 780 - 799
We prove the existence and uniqueness of graphs with prescribed mean curvature function in a large class of Riemannian manifolds which comprises spaces endowed... 
Abstract Harmonic Analysis | 53C42 | Quasilinear elliptic PDE | 53A10 | Conformal Killing graphs | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Mathematics | Dynamical Systems and Ergodic Theory | Differential Geometry | Prescribed mean curvature | Physical Sciences | Science & Technology
Journal Article
Nonlinear analysis, ISSN 0362-546X, 02/2013, Volume 78, Issue 1, pp. 62 - 78
Journal Article
Nonlinear analysis, ISSN 0362-546X, 2010, Volume 72, Issue 11, pp. 4188 - 4199
... of least-energy solutions goes to a point on the boundary ∂ Ω at a rate of o ( ε ) and this point on the boundary approaches a global maximum point of mean curvature... 
Least-energy solution | Quasilinear Neumann problem | Mean curvature [formula omitted]-Laplacian operator | Exponential decay | Mean curvature m-Laplacian operator | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Neumann problem | Positioning | Mathematical analysis | Boundary conditions | Nonlinearity | Complement | Boundaries | Curvature
Journal Article
Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 6/2018, Volume 49, Issue 2, pp. 279 - 312
Journal Article
Mathematical methods in the applied sciences, ISSN 0170-4214, 10/2020, Volume 43, Issue 15, pp. 8496 - 8505
...‐ and supersolution method to find solutions to problem (P). Further, we apply our result to some specific nonlocal prescribed mean curvature problems. 
sub‐ and supersolution method | quasilinear operator | prescribed mean curvature equation | nonlocal problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Mathematical analysis | Curvature
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2011, Volume 250, Issue 2, pp. 675 - 689
... (submitted for publication) [1], the latter in the context of mean curvature type operators, see Theorem 1.3 and Theorems 5.2–5.4 below. Finally, Theorem... 
Entire solutions | Liouville theorems | Quasilinear elliptic inequalities | Physical Sciences | Mathematics | Science & Technology
Journal Article