Results 141 to 150 of about 2,254 (236)
Semilinear elliptic equations with dependence on the gradient
Electronic Journal of Differential Equations, 2012 In this article we consider elliptic equations whose nonlinear term depends on the gradient of the unknown. We assume that the nonlinearity has a asymptotically linear growth at zero and at infinity with respect to the second variable.
Guanggang Liu, Shaoyun Shi, Yucheng Wei
doaj
Optimal energy growth lower bounds for a class of solutions to the vectorial Allen-Cahn equation
, 2014 We prove optimal lower bounds for the growth of the energy over balls of minimizers to the vectorial Allen-Cahn energy in two spatial dimensions, as the radius tends to infinity. In the case of radially symmetric solutions, we can prove a stronger result
Sourdis, Christos
core
Standing Waves in the FitzHugh-Nagumo System and a Problem in Combinatorial Geometry
, 2006 We show that there is a close relation between standing-wave solutions for the FitzHugh-Nagumo system \[ \Delta u +u(u-a)(1-u) - \delta v=0, \ \ \Delta v-\delta \gamma v + u=0 \ \ \mbox{in} \ R^N,\] \[ u, v \to 0 \ \mbox{as} \ |x| \to +\infty ...
Winter, M +3 more
core +1 more source
An inverse boundary-value problem for semilinear elliptic equations
Electronic Journal of Differential Equations, 2010 We show that in dimension two or greater, a certain equivalence class of the scalar coefficient $a(x,u)$ of the semilinear elliptic equation $Delta u,+a(x,u)=0$ is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded ...
Ziqi Sun
doaj
Impulsive fractional order integrodifferential equation via fractional operators. [PDF]
PLoS One, 2023 Al-Omari A, Al-Saadi H.
europepmc +1 more source
Operator compression with deep neural networks. [PDF]
Adv Contin Discret Model, 2022 Kröpfl F, Maier R, Peterseim D.
europepmc +1 more source
Multiplicity results for nonlinear elliptic equations
Electronic Journal of Differential Equations, 2006 Let $Omega$ be a bounded domain in $mathbb{R}^{N}$, $Ngeq 3$, and $p=frac{2N}{N-2}$ the limiting Sobolev exponent. We show that for $fin H^1_0(Omega)^ast$, satisfying suitable conditions, the nonlinear elliptic problem $$displaylines{ -Delta u =|u |^{ p ...
Samira Benmouloud +2 more
doaj
Elastic anisotropy in the reduced Landau-de Gennes model. [PDF]
Proc Math Phys Eng Sci, 2022 Han Y, Harris J, Majumdar A, Zhang L.
europepmc +1 more source
Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities
Electronic Journal of Differential Equations, 2005 We study the existence of positive solutions for a fourth order semilinear elliptic equation under Navier boundary conditions with positive, increasing and convex source term. Both bounded and unbounded solutions are considered. When compared with second
Filippo Gazzola, Elvise Berchio
doaj
On the Normal Stability of Triharmonic Hypersurfaces in Space Forms. [PDF]
J Geom Anal, 2023 Branding V.
europepmc +1 more source