Results 111 to 120 of about 92,595 (298)
Semilinear fractional elliptic equations with gradient nonlinearity involving measures [PDF]
, 2013 We study the existence of solutions to the fractional elliptic equation (E1) $(-\Delta)^\alpha u+\epsilon g(|\nabla u|)=\nu $ in a bounded regular domain $\Omega$ of $\R^N (N\ge2)$, subject to the condition (E2) $u=0$ in $\Omega^c$, where $\epsilon=1$ or
Chen, Huyuan, Veron, Laurent
core +2 more sources
A posteriori error estimation and adaptivity for temporal multiscale problems
PAMM, Volume 24, Issue 4, December 2024.Abstract In science and engineering, problems over multiple scales in time often arise. Two examples are material damage in oscillating structures or plaque growth in pulsating blood vessels. Here the long term effects are of interest but they depend on the coupled fast‐changing physical processes which must be taken into account.
Leopold Lautsch, Thomas Richter
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
Bifurcation for indefinite‐weighted p$p$‐Laplacian problems with slightly subcritical nonlinearity
Mathematische Nachrichten, Volume 297, Issue 11, Page 3982-4002, November 2024.Abstract We study a superlinear elliptic boundary value problem involving the p$p$‐Laplacian operator, with changing sign weights. The problem has positive solutions bifurcating from the trivial solution set at the two principal eigenvalues of the corresponding linear weighted boundary value problem.
Mabel Cuesta, Rosa Pardo
wiley +1 more source
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
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
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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
A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart
, 2020 We establish the nonexistence of nontrivial ancient solutions to the nonlinear heat equation $u_t=\Delta u+|u|^{p-1}u$ which are smaller in absolute value than the self-similar radial singular steady state, provided that the exponent $p$ is strictly ...
Sourdis, Christos
core
Multiple Nontrivial Solutions of Semilinear Elliptic Equations [PDF]
Proceedings of the American Mathematical Society, 1988 We give a condition for a semilinear elliptic equation to have two nontrivial solutions. Our condition does not demand any differentiability of the nonlinear term.
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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