Sub-supersolution theorems for quasilinear elliptic problems: A variational approach
Electronic Journal of Differential Equations, 2004 This paper presents a variational approach to obtain sub - supersolution theorems for a certain type of boundary value problem for a class of quasilinear elliptic partial differential equations.
Vy Khoi Le, Klaus Schmitt
doaj
An Adaptive Multigrid Method for Semilinear Elliptic Equations
East Asian Journal on Applied Mathematics, 2019 An adaptive multigrid method for semilinear elliptic equations based on adaptive multigrid methods and on multilevel correction methods is developed. The solution of a semilinear problem is reduced to a series of linearised elliptic equations on the sequence of adaptive finite element spaces and semilinear elliptic problems on a very low dimensional ...
Xu, Fei +3 more
openaire +2 more sources
Higher-Order Energy Expansions and Spike Locations [PDF]
, 2004 We consider the following singularly perturbed semilinear elliptic problem: (I)\left\{ \begin{array}{l} \epsilon^{2} \Delta u - u + f(u)=0 \ \ \mbox{in} \ \Omega, \\ u>0 \ \ \mbox{in} \ \ \Omega \ \ \mbox{and} \ \frac{\partial u}{\partial \nu}
Winter, M, Wei, J
core +1 more source
Solutions to nonlinear elliptic equations with a nonlocal boundary condition
Electronic Journal of Differential Equations, 2002 We study an elliptic equation and its evolution problem on a bounded domain with nonlocal boundary conditions. Eigenvalue problems, existence, and dynamic behavior of solutions for linear and semilinear equations are investigated.
Yuandi Wang
doaj
The Topological State Derivative: An Optimal Control Perspective on Topology Optimisation. [PDF]
J Geom Anal, 2023 Baumann P, Mazari-Fouquer I, Sturm K.
europepmc +1 more source
Entire solutions of semilinear elliptic equations
Electronic Journal of Differential Equations, 2004 We consider existence of entire solutions of a semilinear elliptic equation $Delta u= k(x) f(u)$ for $x in mathbb{R}^n$, $nge3$. Conditions of the existence of entire solutions have been obtained by different authors.
Alexander Gladkov, Nickolai Slepchenkov
doaj
Classification of positive solutions of semilinear elliptic equations
Comptes Rendus. Mathématique, 2003 We give a classification of all solutions of a general semilinear PDE in the positive quadrant of ℝ 2 .
Busca, J, Efendiev, M, Zelik, S
openaire +3 more sources
Existence of solutions in weighted Sobolev spaces for some degenerate semilinear elliptic equations
, 2004 In this paper, we study existence of solutions to a class of semilinear degenerate elliptic equations in weighted Sobolev ...
Cavalheiro, A.C
core +1 more source
Adaptive pseudo-transient-continuation-Galerkin methods for semilinear elliptic partial differential equations [PDF]
, 2017 In this article, we investigate the application of pseudo-transient-continuation (PTC) schemes for the numerical solution of semilinear elliptic partial differential equations, with possible singular perturbations.
Thomas P. Wihler +4 more
core +1 more source
Multiplicity of Nontrivial Solutions of Semilinear Elliptic Equations
Journal of Mathematical Analysis and Applications, 2000 It is considered the following problem: \(-\Delta u = f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), where \(f\) is a subcritical Carathéodory function. It is proved the existence of at least two nontrivial solutions. This paper unifies and generalizes some results from \textit{A. Castro} and \textit{A. C. Lazer} [Ann. Mat. Pura Appl., IV. Ser.
Liu, Shui-Qiang +2 more
openaire +2 more sources