Results 101 to 110 of about 667 (175)

Multiplicity theorems for resonant and superlinear nonhomogeneous elliptic equations

, 2016
We consider nonlinear elliptic equations driven by the sum of a $p$-Laplacian ($p> 2$) and a Laplacian. We consider two distinct cases. In the first one, the reaction $f(z,\cdot)$ is $(p-1)$-linear near $\pm\infty$ and resonant with respect to a ...
Papageorgiou, Nikolaos S., Rădulescu, Vicenţiu D.   +1 more
core  

A short review on (p,q)-equations with Carathéodory perturbation

Modern Mathematical Methods
We review some recent works dealing with \((p, q)\)-Laplacian equations in the setting of Sobolev spaces and Dirichlet boundary condition. We aim to underline the key role of growth conditions on the Carathéodory perturbation, in establishing both the ...
Calogero Vetro
doaj  

Positive solutions of reaction diffusion equations with super-linear absorption: Universal bounds, uniqueness for the Cauchy problem, boundedness of stationary solutions

Journal of Differential Equations, 2006
It is considered the classical solution \(u \in C^2 (\mathbb R^n \;\times \;(0, \infty)) \cap C(\mathbb R^n \;\times \;[0,\infty))\) to the parabolic problem \[ u_t= Lu+f(x,u), \quad (x,t) \in \mathbb R^n \times (0,\infty), \] \[ u(x,0)= g(x) \geq 0, \quad x \in \mathbb R^n, \] where \[ L=\sum_{i,j=1}^{n} a_{i,j}(x) \frac{\partial^2}{\partial x_i ...
openaire   +2 more sources

Scaling laws in enzyme function reveal a new kind of biochemical universality. [PDF]

Proc Natl Acad Sci U S A, 2022
Gagler DC, Karas B, Kempes CP, Malloy J, Mierzejewski V, Goldman AD, Kim H, Walker SI.   +7 more
europepmc   +1 more source

Uniform large deviation principles of fractional reaction–diffusion equations driven by superlinear multiplicative noise on ℝn

Stochastics and Dynamics
In this paper, we investigate the uniform large deviation principle of the fractional stochastic reaction–diffusion equation on the entire space [Formula: see text] as the noise intensity approaches zero. The nonlinear drift term is dissipative and has a polynomial growth of any order.
openaire   +2 more sources

$L^2$-solutions to stochastic reaction-diffusion equations with superlinear drifts driven by space-time white noise^

Consider the following stochastic reaction-diffusion equation with logarithmic superlinear coefficient b, driven by space-time white noise W: $$ u_t(t,x) = (1/2)u_{xx}(t,x) + b(u(t,x)) + σ(u(t,x))W(dt,dx) $$ for $t > 0$ and $x \in [0,1]$, with initial condition $$ u(0,x) = u_0(x) $$ for $x \in [0,1]$, where $u_0 \in L^2[0,1]$.
Shang, Shijie, Wang, Pengyu, Zhang, Tusheng   +2 more
openaire   +2 more sources

Positive probability of explosion for stochastic heat equation with superlinear accretive reaction term and polynomially growing multiplicative noise

This paper studies the finite time explosion of the stochastic heat equation $\frac{\partial u}{\partial t}(t,x)=\frac{\partial^2}{\partial x^2} u(t,x)+(u(t,x))^β+σ(u(t,x))\dot{W}(t,x)$. We consider an interval $D=[-π,π]$ under periodic boundary condition where $\dot{W}(t,x)$ is a space-time white noise and $σ(u)\approx u^γ$ near $\infty$.
Salins, Michael, Zhang, Yuyang
openaire   +2 more sources

Front propagation in a kinetic reaction-transport equation

, 2013
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction term of ...
Grégoire Nadin, Emeric Bouin, Vincent Calvez   +2 more
core  

Direct Writing of Nanostructured Metasurfaces by Hot-Electron-Driven Laser Sintering. [PDF]

Nano Lett
Chang K, Wei K, Kudtarkar K, Yelkarasi C, Erdemir A, Lan S, Hipwell MC, Pan H.   +7 more
europepmc   +1 more source

Operando recombination kinetics in perovskite nanocrystal films revealed by in situ time-resolved photoluminescence. [PDF]

Nat Commun
Cao D, Jiao Z, Gao J, Wang Y, Ai XC, Zhang JP.   +5 more
europepmc   +1 more source