Results 61 to 70 of about 278 (186)

Semilinear elliptic problems involving Hardy-Sobolev-Maz'ya potential and Hardy-Sobolev critical exponents

Electronic Journal of Differential Equations, 2016
In this article, we study a class of semilinear elliptic equations involving Hardy-Sobolev critical exponents and Hardy-Sobolev-Maz'ya potential in a bounded domain. We obtain the existence of positive solutions using the Mountain Pass Lemma.
Rui-Ting Jiang, Chun-Lei Tang
doaj  

An Adaptive Multigrid Method for Semilinear Elliptic Equations

East Asian Journal on Applied Mathematics, 2019
Summary: 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 ...
Xu, Fei, Huang, Qiumei, Chen, Shuangshuang, Bing, Tao   +3 more
openaire   +2 more sources

Forward uncertainty quantification in random differential equation systems with delta‐impulsive terms: Theoretical study and applications

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7609-7629, 15 May 2025.
This contribution aims at studying a general class of random differential equations with Dirac‐delta impulse terms at a finite number of time instants. Our approach directly addresses calculating the so‐called first probability density function, from which all the relevant statistical information about the solution, a stochastic process, can be ...
Vicente J. Bevia, Juan C. Cortés, Rafael J. Villanueva   +2 more
wiley   +1 more source

Computation of radial solutions of semilinear equations

Electronic Journal of Qualitative Theory of Differential Equations, 2007
We express radial solutions of semilinear elliptic equations on $R^n$ as convergent power series in $r$, and then use Pade approximants to compute both ground state solutions, and solutions to Dirichlet problem.
Philip Korman
doaj   +1 more source

The free boundary for semilinear problems with highly oscillating singular terms

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract We investigate general semilinear (obstacle‐like) problems of the form Δu=f(u)$\Delta u = f(u)$, where f(u)$f(u)$ has a singularity/jump at {u=0}$\lbrace u=0\rbrace$ giving rise to a free boundary. Unlike many works on such equations where f$f$ is approximately homogeneous near {u=0}$\lbrace u = 0\rbrace$, we work under assumptions allowing ...
Mark Allen, Dennis Kriventsov, Henrik Shahgholian   +2 more
wiley   +1 more source

Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems

Electronic Journal of Differential Equations, 1999
When using calculus of variations to study nonlinear elliptic boundary-value problems on unbounded domains, the Palais-Smale condition is not always satisfied.
Chao-Nien Chen, Shyuh-Yaur Tzeng
doaj  

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  

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

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  

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, Tang, Chun-Lei, Wu, Xing-Ping   +2 more
openaire   +2 more sources