Classification of positive solutions of $p$-Laplace equation with a growth term

Matteo Franca

Displaying similar documents to “Classification of positive solutions of $p$ -Laplace equation with a growth term”

Resonance in Preisach systems

Pavel Krejčí (2000)

Applications of Mathematics

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This paper deals with the asymptotic behavior as $t \to \infty$ of solutions $u$ to the forced Preisach oscillator equation $\ddot{w} (t) + u (t) = ψ (t)$ , $w = u + 𝒫 [u]$ , where $𝒫$ is a Preisach hysteresis operator, $ψ \in L^{\infty} (0, \infty)$ is a given function and $t \geq 0$ is the time variable. We establish an explicit asymptotic relation between the Preisach measure and the function $ψ$ (or, in a more physical terminology, a balance condition between the hysteresis dissipation and the external forcing) which guarantees that every solution remains bounded for all times. Examples...

Motion with friction of a heavy particle on a manifold. Applications to optimization

Alexandre Cabot (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Let $Φ : H \to ℝ$ be a $𝒞^{2}$ function on a real Hilbert space and $Σ \subset H \times ℝ$ the manifold defined by $Σ : =$ Graph $(Φ)$ . We study the motion of a material point with unit mass, subjected to stay on $Σ$ and which moves under the action of the gravity force (characterized by $g > 0$ ), the reaction force and the friction force ( $γ > 0$ is the friction parameter). For any initial conditions at time $t = 0$ , we prove the existence of a trajectory $x (.)$ defined on $ℝ_{+}$ . We are then interested in the asymptotic behaviour of the trajectories when $t \to + \infty$ . More...

On Kirchhoff type problems involving critical and singular nonlinearities

Chun-Yu Lei, Chang-Mu Chu, Hong-Min Suo, Chun-Lei Tang (2015)

Annales Polonici Mathematici

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In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧ $- (a + b \int_{Ω} | \nabla u | ² d x) Δ u = u ⁵ + λ u^{q - 1} / {| x |}^{β}$ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.

Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations

Peter Poláčik (2002)

Mathematica Bohemica

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We consider three types of semilinear second order PDEs on a cylindrical domain $Ω \times (0, \infty)$ , where $Ω$ is a bounded domain in $ℝ^{N}$ , $N \geq 2$ . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of $Ω \times (0, \infty)$ is reserved for time $t$ , the third type is an elliptic equation with a singled out unbounded variable $t$ . We discuss the asymptotic behavior, as $t \to \infty$ , of solutions which are defined and bounded on $Ω \times (0, \infty)$ .

Displaying similar documents to “Classification of positive solutions of p -Laplace equation with a growth term”

Resonance in Preisach systems

Motion with friction of a heavy particle on a manifold. Applications to optimization

On Kirchhoff type problems involving critical and singular nonlinearities

Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations

Displaying similar documents to “Classification of positive solutions of $p$ -Laplace equation with a growth term”