LAUSR

Gradient estimates of mean curvature equation with Neumann boundary condition in domains of Riemannian manifold

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0 Published in 2017 at "International Journal of Mathematics"

DOI: 10.1142/s0129167x17500653

Abstract: We study the prescribed mean curvature equation with Neumann boundary conditions in domains of Riemannian manifold. The main goal is to establish the gradient estimates for solutions by the maximum principle. As a consequence, we… read more here.

Keywords: domains riemannian; mean curvature; neumann boundary; equation neumann ... See more keywords

Existence and multiplicity of positive solutions of a one-dimensional mean curvature equation in Minkowski space

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0 Published in 2018 at "Boundary Value Problems"

DOI: 10.1186/s13661-018-0963-5

Abstract: In this paper, we consider a one-dimensional mean curvature equation in Minkowski space and the corresponding one-parameter problem. By using a fixed point theorem of cone expansion and compression of norm type, the existence and… read more here.

Keywords: mean curvature; equation minkowski; one dimensional; minkowski space ... See more keywords

Bifurcation curve for the Minkowski-curvature equation with concave or geometrically concave nonlinearity

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0 Published in 2024 at "Boundary Value Problems"

DOI: 10.1186/s13661-024-01906-7

Abstract: We study the bifurcation curve and exact multiplicity of positive solutions in the space C 2 ( ( − L , L ) ) ∩ C ( [ − L , L ] ) $C^{2}\left… read more here.

Keywords: minkowski curvature; bifurcation curve; bifurcation; geometrically concave ... See more keywords

Exact Solution and Bifurcation Curve for the Minkowski-Curvature Equation with Nonlinearity up+uq, p > 1

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0 Published in 2025 at "Mathematics"

DOI: 10.3390/math13223680

Abstract: We study the bifurcation curve and exact multiplicity of positive solutions in the space C2(−L,L)∩C[−L,L] for the Minkowski-curvature equation: −u′(x)1−u′(x)2′=λup+uq,−L1. If 1 read more here.

Keywords: curvature equation; minkowski curvature; bifurcation curve; bifurcation ... See more keywords

The interior gradient estimate of prescribed Hessian quotient curvature equation in the hyperbolic space

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0 Published in 2021 at "Communications on Pure and Applied Analysis"

DOI: 10.3934/cpaa.2021012

Abstract: In this paper, we obtain the interior gradient estimate of the Hessian quotient curvature equation in the hyperbolic space. The method depends on the maximum principle. read more here.

Keywords: quotient curvature; interior gradient; gradient estimate; curvature equation ... See more keywords