Results 111 to 120 of about 1,398 (233)
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
On a semilinear elliptic equation with inverse square potential
, 2008 On a semilinear elliptic equation with inverse square ...
Dupaigne, Louis +2 more
core +2 more sources
A Higher-Order Energy Expansion to Two-Dimensional Singularly Neumann Problems
, 2005 Of concern is the following singularly perturbed semilinear elliptic problem \begin{equation*} \left\{ \begin{array}{c} \mbox{${\epsilon}^2\Delta u -u+u^p =0$ in $\Omega$}\\ \mbox{$u>0$ in $\Omega$ and $
Yeung, W-K, Winter, M, Wei, J
core
Multiplicity of solutions for elliptic boundary value problems
Electronic Journal of Differential Equations, 2014 In this article, we study the existence of infinitely many solutions for the semilinear elliptic equation $-\Delta u+a(x)u=f(x,u)$ in a bounded domain of $\mathbb{R}^N$ $(N\geq 3)$ with the Dirichlet boundary conditions, where the primitive of the ...
Yiwei Ye
doaj
Existence of positive solutions for Dirichlet problems of some singular elliptic equations
Electronic Journal of Differential Equations, 2003 When an unbounded domain is inside a slab, existence of a positive solution is proved for the Dirichlet problem of a class of semilinear elliptic equations similar to the singular Emden-Fowler equation.
Zhiren Jin
doaj
A singular perturbation result for a class of periodic-parabolic BVPs
Open MathematicsIn this article, we obtain a very sharp version of some singular perturbation results going back to Dancer and Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag,
Cano-Casanova Santiago +2 more
doaj +1 more source
Clustered spots in the FitzHugh-Nagumo system
, 2004 We construct {\bf clustered} spots for the following FitzHugh-Nagumo system: \[\left\{\begin{array}{l}\ep^2\Delta u +f(u)-\delta v =0\quad \mbox{in} \ \Om,\\[2mm]\Delta v+ u=0 \quad \mbox{in} \ \Om,\\[2mm] u= v =0 \quad\mbox{on} \ \partial \Om, \end{
Winter, M +5 more
core +1 more source
Positive single rupture solutions to a semilinear elliptic equation
, 2005 The existence of positive single rupture solutions to the semilinear elliptic equation Δu=f(u) with f(0)=∞ in a finite ball is obtained via the Pohozaev ...
Li, Ke, Guo, Zongming, Guo, Hongxia
core +1 more source
A semilinear control problem involving homogenization
Electronic Journal of Differential Equations, 2001 We consider a control problem involving a semilinear elliptic equation with a uniformly Lipschitz non-linearity and rapidly oscillating coefficients in a bounded domain of $mathbb{R}^N$.
Carlos Conca +2 more
doaj
Multi-Peak Solutions for a Wide Class of Singular Perturbation Problems
, 1999 In this paper we are concerned with a wide class of singular perturbation problems arising from such diverse fields as phase transitions, chemotaxis, pattern formation, population dynamics and chemical reaction theory.
Winter, M +3 more
core