scholarly journals Stability of standing waves for monostable reaction–convection equations in a large bounded domain with boundary conditions

2013 ◽  
Vol 255 (1) ◽  
pp. 58-84 ◽  
Author(s):  
Xiao-Biao Lin
Keyword(s):  
Boundary Conditions ◽  
Bounded Domain ◽  
Standing Waves

scholarly journals From metaphors to equations: How can we find the good ones?

2000 ◽  
Vol 23 (3) ◽  
pp. 409-410
Author(s):  
Gottfried Mayer-Kress
Keyword(s):  
Boundary Conditions ◽  
Forest Fire ◽  
Water Waves ◽  
Standing Waves ◽  
Musical Instruments ◽  
Oscillator Model ◽  
Mechanical Oscillator ◽  
Target Article ◽  
Mechanical Oscillators

Among the metaphors used in the target article are “musical instruments,” “water waves,” and other types of mechanical oscillators. The corresponding equations have inertial properties and lead to standing waves that depend on boundary conditions. Other, physiologically relevant quantities like refractory times are not contained in the mechanical oscillator model but occur naturally, for instance, in biological forest fire metaphors.

Multiple solutions for a non-homogeneous elliptic equation at the critical exponent

2004 ◽  
Vol 134 (1) ◽  
pp. 69-87 ◽  
Author(s):  
Mónica Clapp ◽  
Manuel Del Pino ◽  
Monica Musso
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Critical Exponent ◽  
Bounded Domain ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Sign Changing Solutions ◽  
Homogeneous Elliptic Equation

We consider the equation−Δu = |u|4/(N−2)u + εf(x) under zero Dirichlet boundary conditions in a bounded domain Ω in RN exhibiting certain symmetries, with f ≥ 0, f ≠ 0. In particular, we find that the number of sign-changing solutions goes to infinity for radially symmetric f, as ε → 0 if Ω is a ball. The same is true for the number of negative solutions if Ω is an annulus and the support of f is compact in Ω.

Analysis of an elliptic system with infinitely many solutions

2017 ◽  
Vol 6 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Carmen Cortázar ◽  
Manuel Elgueta ◽  
Jorge García-Melián
Keyword(s):  
Boundary Conditions ◽  
Elliptic System ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Infinitely Many Solutions ◽  
Smooth Bounded Domain ◽  
Content Type ◽  
Outward Unit ◽  
Unit Normal

AbstractWe consider the elliptic system ${\Delta u\hskip-0.284528pt=\hskip-0.284528ptu^{p}v^{q}}$, ${\Delta v\hskip-0.284528pt=\hskip-0.284528ptu^{r}v^{s}}$ in Ω with the boundary conditions ${{\partial u/\partial\eta}=\lambda u}$, ${{\partial v/\partial\eta}=\mu v}$ on ${\partial\Omega}$, where Ω is a smooth bounded domain of ${\mathbb{R}^{N}}$, ${p,s>1}$, ${q,r>0}$, ${\lambda,\mu>0}$ and η stands for the outward unit normal. Assuming the “criticality” hypothesis ${(p-1)(s-1)=qr}$, we completely analyze the values of ${\lambda,\mu}$ for which there exist positive solutions and give a detailed description of the set of solutions.

scholarly journals A Note on Sign-Changing Solutions to the NLS on the Double-Bridge Graph

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 161
Author(s):  
Diego Noja ◽  
Sergio Rolando ◽  
Simone Secchi
Keyword(s):  
Boundary Conditions ◽  
Standing Waves ◽  
Nls Equation ◽  
Sign Changing Solutions

We study standing waves of the NLS equation posed on the double-bridge graph: two semi-infinite half-lines attached at a circle. At the two vertices, Kirchhoff boundary conditions are imposed. We pursue a recent study concerning solutions nonzero on the half-lines and periodic on the circle, by proving some existing results of sign-changing solutions non-periodic on the circle.

scholarly journals A biharmonic equation with singular nonlinearity

2011 ◽  
Vol 55 (1) ◽  
pp. 155-166 ◽  
Author(s):  
Marius Ghergu
Keyword(s):  
Green Function ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Existence And Uniqueness ◽  
Biharmonic Equation ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Biharmonic Operator ◽  
The Green Function ◽  
Uniqueness Of A Solution

AbstractWe study the biharmonic equation Δ2u=u−α, 0 < α < 1, in a smooth and bounded domain Ω ⊂ ℝn,n≥ 2, subject to Dirichlet boundary conditions. Under some suitable assumptions on Ω related to the positivity of the Green function for the biharmonic operator, we prove the existence and uniqueness of a solution.

Sign in / Sign up

Export Citation Format

Share Document