Uniqueness of solutions of some elliptic equations without condition at infinity

2002 ◽  
Vol 335 (9) ◽  
pp. 739-744 ◽  
Author(s):  
Alessio Porretta
Keyword(s):  
Elliptic Equations ◽  
Uniqueness Of Solutions

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 Prescribed conditions at infinity for fractional parabolic and elliptic equations with unbounded coefficients

2018 ◽  
Vol 24 (1) ◽  
pp. 105-127
Author(s):  
Fabio Punzo ◽  
Enrico Valdinoci
Keyword(s):  
Asymptotic Behavior ◽  
Parabolic Equations ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Time Dependent ◽  
Uniqueness Of Solutions ◽  
Unbounded Coefficients ◽  
Conditions At Infinity

We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed point-wise conditions at infinity (in space), which can be time-dependent. Moreover, we study the asymptotic behavior of such solutions. We also consider solutions of elliptic equations satisfying appropriate conditions at infinity.

Existence and uniqueness of solutions of an A-harmonic elliptic equation

2019 ◽  
Vol 56 (1) ◽  
pp. 13-21
Author(s):  
Mouna Kratou
Keyword(s):  
Weak Solution ◽  
Elliptic Equation ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions

Abstract This paper deals with the existence and uniqueness of weak solution of a problem which involves a class of A-harmonic elliptic equations of nonhomogeneous type. Under appropriate assumptions on the function f, our main results are obtained by using Browder Theorem.

A p(x)-Laplacian extension of the Díaz-Saa inequality and some applications

2019 ◽  
Vol 150 (1) ◽  
pp. 205-232 ◽  
Author(s):  
Peter Takáč ◽  
Jacques Giacomoni
Keyword(s):  
Elliptic Equations ◽  
Energy Functional ◽  
Quasilinear Elliptic Equations ◽  
Uniqueness Of Solutions ◽  
Comparison Principles ◽  
Convexity Properties ◽  
Quasilinear Elliptic

AbstractThe main result of this work is a new extension of the well-known inequality by Díaz and Saa which, in our case, involves an anisotropic operator, such as the p(x)-Laplacian, $\Delta _{p(x)}u\equiv {\rm div}( \vert \nabla u \vert ^{p(x)-2}\nabla u)$. Our present extension of this inequality enables us to establish several new results on the uniqueness of solutions and comparison principles for some anisotropic quasilinear elliptic equations. Our proofs take advantage of certain convexity properties of the energy functional associated with the p(x)-Laplacian.

scholarly journals Existence and uniqueness of solutions for a semilinear elliptic system

2005 ◽  
Vol 2005 (10) ◽  
pp. 1507-1523 ◽  
Author(s):  
Robert Dalmasso
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Biharmonic Equation ◽  
Nonlinear Elliptic Equations ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System ◽  
Homogeneous Dirichlet Problem

We consider the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary conditions. In a particular case, the system reduces to the homogeneous Dirichlet problem for the biharmonic equationΔ2u=|u|pin a ball withp>0.

scholarly journals Numerical solution of nonlinear elliptic systems by block monotone iterations

2019 ◽  
Vol 60 ◽  
pp. C79-C94
Author(s):  
Mohamed Saleh Mehdi Al-Sultani ◽  
Igor Boglaev
Keyword(s):  
Iterative Methods ◽  
Elliptic Equations ◽  
Numerical Solutions ◽  
Upper And Lower Solutions ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Equations ◽  
Difference Schemes ◽  
Uniqueness Of Solutions ◽  
Monotone Iterative ◽  
Nonlinear Elliptic

We present numerical methods for solving a coupled system of nonlinear elliptic problems, where reaction functions are quasimonotone nondecreasing. We utilize block monotone iterative methods based on the Jacobi and Gauss--Seidel methods incorporated with the upper and lower solutions method. A convergence analysis and the theorem on uniqueness of solutions are discussed. Numerical experiments are presented. References Boglaev, I., Monotone iterates for solving systems of semilinear elliptic equations and applications, ANZIAM J, Proceedings of the 8th Biennial Engineering Mathematics and Applications Conference, EMAC-2007, 49(2008), C591C608. doi:10.21914/anziamj.v49i0.311 Pao, C. V., Nonlinear parabolic and elliptic equations, Springer-Verlag (1992). doi:10.1007/978-1-4615-3034-3 Pao, C. V., Block monotone iterative methods for numerical solutions of nonlinear elliptic equations, Numer. Math., 72(1995), 239262. doi:10.1007/s002110050168 Samarskii, A., The theory of difference schemes, CRC Press (2001). https://www.crcpress.com/The-Theory-of-Difference-Schemes/Samarskii/p/book/9780824704681 Varga, R. S., Matrix iterative analysis, Springer-Verlag (2000). doi:10.1007/978-3-642-05156-2

Sign in / Sign up

Export Citation Format

Share Document