scholarly journals Some existence results on the exterior Dirichlet problem for the minimal hypersurface equation

2011 ◽  
Vol 28 (3) ◽  
pp. 385-393 ◽  
Author(s):  
Nedir do Espírito-Santo ◽  
Jaime Ripoll
Keyword(s):  
Dirichlet Problem ◽  
Minimal Hypersurface ◽  
Existence Results

scholarly journals Variational Method to p-Laplacian Fractional Dirichlet Problem with Instantaneous and Noninstantaneous Impulses

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Yiru Chen ◽  
Haibo Gu ◽  
Lina Ma
Keyword(s):  
Dirichlet Problem ◽  
Variational Method ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Major Result ◽  
Dirichlet Boundary Value Problem ◽  
Fractional Differential ◽  
Noninstantaneous Impulses

In this paper, a research has been done about the existence of solutions to the Dirichlet boundary value problem for p-Laplacian fractional differential equations which include instantaneous and noninstantaneous impulses. Based on the critical point principle and variational method, we provide the equivalence between the classical and weak solutions of the problem, and the existence results of classical solution for our equations are established. Finally, an example is given to illustrate the major result.

Hermitian Yang–Mills–Higgs Metrics on Complete Kähler Manifolds

2005 ◽  
Vol 57 (4) ◽  
pp. 871-896 ◽  
Author(s):  
Xi Zhang
Keyword(s):  
Dirichlet Problem ◽  
Einstein Equation ◽  
Existence Results ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Vortex Equation ◽  
Vortex Equations ◽  
Yang Mills

AbstractIn this paper, first, we will investigate the Dirichlet problem for one type of vortex equation, which generalizes the well-known Hermitian Einstein equation. Secondly, we will give existence results for solutions of these vortex equations over various complete noncompact Kähler manifolds.

scholarly journals On the Asymptotic Dirichlet Problem for the Minimal Hypersurface Equation in a Hadamard Manifold

2017 ◽  
Vol 47 (4) ◽  
pp. 485-501 ◽  
Author(s):  
Jean-Baptiste Casteras ◽  
Ilkka Holopainen ◽  
Jaime B. Ripoll
Keyword(s):  
Dirichlet Problem ◽  
Minimal Hypersurface ◽  
Hadamard Manifold

Existence results for the Dirichlet problem of some degenerate nonlinear elliptic equations

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic

AbstractIn this paper we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated to the degenerate nonlinear elliptic equations

scholarly journals Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations

2019 ◽  
Vol 5 (2) ◽  
pp. 164-178
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Degenerate Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

AbstractIn this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations\left\{ {\matrix{ { - {\rm{div}}\left[ {\mathcal{A}\left( {x,\nabla u} \right){\omega _1} + \mathcal{B}\left( {x,u,\nabla u} \right){\omega _2}} \right] = {f_0}\left( x \right) - \sum\limits_{j = 1}^n {{D_j}{f_j}\left( x \right)\,\,{\rm{in}}} \,\,\,\,\,\Omega ,} \hfill \cr {u\left( x \right) = 0\,\,\,\,{\rm{on}}\,\,\,\,\partial \Omega {\rm{,}}} \hfill \cr } } \right.in the setting of the weighted Sobolev spaces.

scholarly journals Existence results for nonlinear elliptic problems on fractal domains

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Massimiliano Ferrara ◽  
Giovanni Molica Bisci ◽  
Dušan Repovš
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Critical Point ◽  
Elliptic Problems ◽  
Open Interval ◽  
Existence Results ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Fractal Domains ◽  
Critical Point Result

AbstractSome existence results for a parametric Dirichlet problem defined on the Sierpiński fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well-determined open interval of positive eigenvalues for which the problem admits at least one non-trivial weak solution.

Comparison and Existence Results for Classes of Nonlinear Elliptic Equations with General Growth in the Gradient

2007 ◽  
Vol 7 (1) ◽  
Author(s):  
Vincenzo Ferone ◽  
Basilio Messano
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Principal Term ◽  
Existence Results ◽  
Nonlinear Elliptic ◽  
General Growth

AbstractIn this paper we study the Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = H(x, u, Du), where the principal term is a Leray-Lions operator defined on W

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