Results 31 to 40 of about 211,213 (315)
Discrete & Continuous Dynamical Systems - B, 2018 In this paper we study global bifurcation phenomena for the Dirichlet problem associated with the prescribed mean curvature equation in Minkowski space \begin{document}$\left\{ \begin{array}{l} -\text{div}\big(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\big) =
Ruyun Ma, Man Xu
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Periodic solutions for nonlinear equations with mean curvature-like operators
Applied Mathematics Letters, 2006 AbstractWe give an existence result for a periodic boundary value problem involving mean curvature-like operators in the scalar case. Following [R. Manásevich, J. Mawhin, Periodic solutions for nonlinear systems with p-Laplacian-like operators, J. Differential Equations 145 (1998), 367–393], we use an approach based on the Leray–Schauder degree.
Pierluigi Benevieri +2 more
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Electronic Research ArchiveIn this paper, we establish the existence of two positive solutions for a discrete mean curvature problem with Dirichlet boundary value conditions. The approach is based on a two-critical-point theorem.
Liqun Jiang, Lin Zou, Xiaoyan Chen
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Positive decaying solutions to BVPs with mean curvature operator
, 2017 A nonlocal boundary value problem on the half-closed interval, associated to differential equations with the Euclidean mean curvature operator or with the Minkowski mean curvature operator is here considered. By using a new approach, based on a linearization device and some properties of principal solutions of certain disconjugate second-order linear ...
Z. Došlá, M. Marini, S. Matucci
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Commutators, eigenvalue gaps, and mean curvature in the theory of Schr\"odinger operators [PDF]
Communications in Partial Differential Equations, 2003 Commutator relations are used to investigate the spectra of Schr dinger Hamiltonians, $H = - + V({x}),$ acting on functions of a smooth, compact $d$-dimensional manifold $M$ immersed in $\bbr^ , \geq d+1$. Here $ $ denotes the Laplace-Beltrami operator, and the real-valued potential--energy function $V(x)$ acts by multiplication. The manifold $M$
Harrell, Mogoi Evans
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Mean curvature and shape operator of isometric immersions in real-space-forms [PDF]
Glasgow Mathematical Journal, 1996 According to the well-known Nash's theorem, every Riemannian n-manifold admits an isometric immersion into the Euclidean space En(n+1)(3n+11)/2. In general, there exist enormously many isometric immersions from a Riemannian manifold into Euclidean spaces if no restriction on the codimension is made.
Bang‐Yen Chen
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Nodal solutions to problem with mean curvature operator in Minkowski space
Differential and Integral Equations, 2017 This paper is devoted to investigate the existence and multiplicity of radial nodal solutions for the following Dirichlet problem with mean curvature operator in Minkowski space \begin{eqnarray} \begin{cases} -\text{div} \Big (\frac{\nabla v}{\sqrt{1-\vert \nabla v\vert^2}} \Big ) = \lambda f(\vert x\vert,v)\,\, &\text{in}\,\, B_R(0),\\ v=0~~~~~~~~~~~~~
Guowei Dai, Jun Wang
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Journal of Applied Analysis & ComputationSummary: In this work, we study an Ambrosetti-Prodi type results for discrete Minkowski-mean curvature operators with repulsive singularities \[ \begin{aligned} &\Delta \left( \frac{\Delta u(t-1)}{\sqrt{1-(\Delta u(t-1))^2}} \right) + f(u) \Delta u(t) + g(t,u (t)) = s, \quad t \in [1,T]_{\mathbb{Z}},\\ &u(0) = u(T), \quad \Delta u(0) = \Delta u(T ...
Yaqin Li, Yanqiong Lu
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On timelike hypersurfaces of the Minkowski 4-space with 1-proper second mean curvature vector [PDF]
Journal of Mahani Mathematical Research, 2023 The mean curvature vector field of a submanifold in the Euclidean $n$-space is said to be $proper$ if it is an eigenvector of the Laplace operator $\Delta$.
Firooz Pashaie +3 more
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