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Several Liouville-type theorems are presented for stable solutions of the equation $- Δ u = f (u)$ in $ℝ^{N}$ , where $f > 0$ is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are discussed.

Stagnation zones of ideal flows in long and narrow bands.

Miklyukov, V.M., Chow, S.-S., Solovjov, V.P. (2004)

International Journal of Mathematics and Mathematical Sciences

Stark stetige Halbgruppen und Gruppen als Lösungen von Cauchy-Problemen in der Mathematischen Physik.

J. Hejtmanek (1976)

Monatshefte für Mathematik

Stationary p-harmonic maps into spheres

Paweł Strzelecki (1996)

Banach Center Publications

Stationary radial solutions for a quasilinear Cahn-Hilliard model in $N$ space dimensions.

Takáč, Peter (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions.

Chipot, M., Fila, M., Quittner, P. (1991)

Acta Mathematica Universitatis Comenianae. New Series

Stationary solutions for a Schrödinger-Poisson system in $ℝ^{3}$ .

Benmlih, Khalid (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Stationary solutions for the Cahn-Hilliard equation

Juncheng Wei, Matthias Winter (1998)

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

Stationary solutions of the generalized Smoluchowski-Poisson equation

Robert Stańczy (2008)

Banach Center Publications

The existence of steady states in the microcanonical case for a system describing the interaction of gravitationally attracting particles with a self-similar pressure term is proved. The system generalizes the Smoluchowski-Poisson equation. The presented theory covers the case of the model with diffusion that obeys the Fermi-Dirac statistic.

Stationary solutions of two-dimensional heterogeneous energy models with multiple species

Annegret Glitzky, Rolf Hünlich (2004)

Banach Center Publications

We investigate stationary energy models in heterostructures consisting of continuity equations for all involved species, of a Poisson equation for the electrostatic potential and of an energy balance equation. The resulting strongly coupled system of elliptic differential equations has to be supplemented by mixed boundary conditions. If the boundary data are compatible with thermodynamic equilibrium then there exists a unique steady state. We prove that in a suitable neighbourhood of such a thermodynamic...

Stationary Solutions to the Navier-Stokes Equations in Dimension Four.

Claus Gerhardt (1979)

Mathematische Zeitschrift

Stationary states for a two-dimensional singular Schrödinger equation

Paolo Caldiroli, Roberta Musina (2001)

Bollettino dell'Unione Matematica Italiana

In questo articolo studiamo problemi di Dirichlet singolari, lineari e semilineari, della forma ${|x|}^{2} Δ u = f (u)$ in $Ω$ , $u = 0$ su $\partial Ω$ , dove $Ω$ è un dominio in $R^{2}$ e $f (u) = λ u$ o $f (u) = λ u + {|u|}^{p - 2} u$ con $p > 2$ (o nonlinearità più generali). In tali problemi bidimensionali emergono alcune difficoltà a causa della non validità della disuguaglianza di Hardy in $R^{2}$ e a causa delle invarianze dell'equazione $- {|x|}^{2} Δ u = f (u)$ . Pertanto opportune condizioni su $λ$ e $Ω$ sono necessarie al fine di garantire l'esistenza di una soluzione positiva. Per esempio, se $Γ_{0}$ è una curva non costante...

Steady Boussinesq system with mixed boundary conditions including friction conditions

Tujin Kim (2022)

Applications of Mathematics

In this paper we are concerned with the steady Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak, one-sided leak, velocity, vorticity, pressure and stress conditions together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions, it is proved that if the data of the problem are small enough, then there exists a solution...

Steady state coexistence solutions of reaction-diffusion competition models

Joon Hyuk Kang, Jungho Lee (2006)

Czechoslovak Mathematical Journal

Two species of animals are competing in the same environment. Under what conditions do they coexist peacefully? Or under what conditions does either one of the two species become extinct, that is, is either one of the two species excluded by the other? It is natural to say that they can coexist peacefully if their rates of reproduction and self-limitation are relatively larger than those of competition rates. In other words, they can survive if they interact strongly among themselves and weakly...

Steady vortex flows obtained from a constrained variational problem.

Emamizadeh, B., Mehrabi, M.H. (2002)

International Journal of Mathematics and Mathematical Sciences

Steady-state buoyancy-driven viscous flow with measure data

Tomáš Roubíček (2001)

Mathematica Bohemica

Steady-state system of equations for incompressible, possibly non-Newtonean of the $p$ -power type, viscous flow coupled with the heat equation is considered in a smooth bounded domain $Ω \subset ℝ^{n}$ , $n = 2$ or 3, with heat sources allowed to have a natural $L^{1}$ -structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if $p > 3 / 2$ (for $n = 2$ ) or if $p > 9 / 5$ (for $n = 3$ ).

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