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
Uniqueness of singular solution of semilinear elliptic equation [PDF]
arXiv, 2010 In this paper, we study asymptotic behavior of solution near 0 for a class of elliptic problem.
arxiv
Existence of a solution to a semilinear elliptic equation
AIMS Mathematics, 2016 We consider the equation $-\Delta u =f(u)-\frac{1}{|\Omega|}\int_{\Omega} f(u)d\mathbf{x}$, where the domain $\Omega= \mathbb{T}^N$, the $N$-dimensional torus, with $N=2$ or $N=3$. And $f$ is a given smooth function of $u$ for$u(\mathbf{x}) \in G \subset \mathbb{R}$.
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Uniqueness of positive solutions to semilinear elliptic equations with double power nonlinearities, revised eddition [PDF]
arXiv, 2009 We consider uniqueness of positive solutions to semilinear elliptic equations with double power nonlinearities. The condition to assure the existence of positive solutions to these types of equations has long been known. On the other hand for uniqueness, quite technical additional condition is proposed by Ouyang and Shi in 1998. In the present paper we
arxiv
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
On the solution stability of parabolic optimal control problems. [PDF]
Comput Optim Appl, 2023 Corella AD, Jork N, Veliov VM.
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Nonexistence of nonconstant global minimizers with limit at $\infty$ of semilinear elliptic equations in all of $R^N$ [PDF]
arXiv, 2009 We prove nonexistence of nonconstant global minimizers with limit at infinity of the semilinear elliptic equation $-\Delta u=f(u)$ in the whole $R^N$, where $f\in C^1(R)$ is a general nonlinearity and $N\geq 1$ is any dimension. As a corollary of this result, we establish nonexistence of nonconstant bounded radial global minimizers of the previous ...
arxiv
Cesari-type Conditions for Semilinear Elliptic Equations with Leading Term Containing Controls [PDF]
arXiv, 2010 An optimal control problem governed by semilinear elliptic partial differential equations is considered. The equation is in divergence form with the leading term containing controls. By studying the $G$-closure of the leading term, an existence result is established under a Cesari-type condition.
arxiv
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
Critical blowup exponent to a class of semilinear elliptic equations with constraints in higher dimension - local properties [PDF]
arXiv, 2014 We study a class of semilinear elliptic equations with constraints in higher dimension. It is known that several mathematical structures of the problem are closed to those of the Liouville equation in dimension two. In this paper, we establish a classification of entire solutions, the $\sup + \inf$ type inequality and the quantized blowup mechanism.
arxiv