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We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in an Ls-neighborhood of a reference function whereby the underlying analysis allows...

Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order

Michael G. Crandall (1989)

Annales de l'I.H.P. Analyse non linéaire

Semilinear Dirichlet problem with nearly critical exponent asymptotic location of Hot spots.

Martin Flucher, W. Juncheng (1997)

Manuscripta mathematica

Semilinear elliptic eigenvalue problems on an infinite strip with an application to stratified fluids

Charles J. Amick (1984)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Semilinear elliptic equations having asymptotic limits at zero and infinity.

Perera, Kanishka, Schechter, Martin (1999)

Abstract and Applied Analysis

Semilinear elliptic equations in unbounded domain of $ℝ^{N}$ . (Équations elliptiques semi linéaires dans des domaines non bornés de $ℝ^{N}$ .)

Khodja, B. (1996)

Portugaliae Mathematica

Semilinear Elliptic Equations on Unbounded Domains.

G.R. Burton (1985)

Mathematische Zeitschrift

Semilinear elliptic problems with nonlinearities depending on the derivative

David Arcoya, Naira del Toro (2003)

Commentationes Mathematicae Universitatis Carolinae

We deal with the boundary value problem $\begin{matrix} - Δ u (x) & = λ_{1} u (x) + g (\nabla u (x)) + h (x), & x \in Ω u (x) & = 0, & x \in \partial Ω \end{matrix}$ where $Ω \subset ℝ^{N}$ is an smooth bounded domain, $λ_{1}$ is the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary conditions on $Ω$ , $h \in L^{max {2, N / 2}} (Ω)$ and $g : ℝ^{N} ⟶ ℝ$ is bounded and continuous. Bifurcation theory is used as the right framework to show the existence of solution provided that $g$ satisfies certain conditions on the origin and at infinity.

Semilinear problems with bounded nonlinear term.

Schechter, Martin (2005)

Boundary Value Problems [electronic only]

Semiregular finite elements in solving some nonlinear problems

Jana Zlámalová (2001)

Applications of Mathematics

In this paper, under the maximum angle condition, the finite element method is analyzed for nonlinear elliptic variational problem formulated in [4]. In [4] the analysis was done under the minimum angle condition.

Sharp L...-Error Estimates for Semilinear Elliptic Problems with Free Boundaries.

Ricardo H. Nochetto (1989)

Numerische Mathematik

Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem

Angela Pistoia, Tobias Weth (2007)

Annales de l'I.H.P. Analyse non linéaire

Sign changing solutions for elliptic equations with critical growth in cylinder type domains

Pedro Girão, Miguel Ramos (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the existence of positive and of nodal solutions for $- Δ u = {| u |}^{p - 2} u + μ {| u |}^{q - 2} u$ , $u \in H_{0}^{1} (Ω)$ , where $μ > 0$ and $2 < q < p = 2 N (N - 2)$ , for a class of open subsets $Ω$ of $ℝ^{N}$ lying between two infinite cylinders.

Sign changing solutions for elliptic equations with critical growth in cylinder type domains

Pedro Girão, Miguel Ramos (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the existence of positive and of nodal solutions for -Δu = |u|p-2u + µ|u|q-2u, $u \in H_{0}^{1} (Ω)$ , where µ > 0 and 2 < q < p = 2N(N - 2) , for a class of open subsets Ω of $ℝ^{N}$ lying between two infinite cylinders.

Sign-changing and multiple solutions for the $p$ -Laplacian.

Carl, Siegfried, Perera, Kanishka (2002)

Abstract and Applied Analysis

Single blow-up solutions for a slightly subcritical biharmonic equation.

El Mehdi, Khalil (2006)

Abstract and Applied Analysis

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