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 → ∞ of solutions u to the forced Preisach oscillator equation w ¨ ( t ) + u ( t ) = ψ ( t ) , w = u + 𝒫 [ u ] , where 𝒫 is a Preisach hysteresis operator, ψ ∈ L ∞ ( 0 , ∞ ) is a given function and t ≥ 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 → ℝ be a 𝒞 2 function on a real Hilbert space and Σ ⊂ H × 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 → + ∞ . 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 ∫ Ω | ∇ 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 × ( 0 , ∞ ) , where Ω is a bounded domain in ℝ N , N ≥ 2 . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of Ω × ( 0 , ∞ ) 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 → ∞ , of solutions which are defined and bounded on Ω × ( 0 , ∞ ) .

Monotonicity and symmetry of solutions of p -Laplace equations, 1 < p < 2 , via the moving plane method

Lucio Damascelli, Filomena Pacella (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We present some monotonicity and symmetry results for positive solutions of the equation - div ⁢ D ⁢ u p - 2 ⁢ D ⁢ u = f ⁢ u satisfying an homogeneous Dirichlet boundary condition in a bounded domain Ω . We assume 1 < p < 2 and f locally Lipschitz continuous and we do not require any hypothesis on the critical set of the solution. In particular we get that if Ω is a ball then the solutions are radially symmetric and strictly radially decreasing.

Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent

Jia-Feng Liao, Jiu Liu, Peng Zhang, Chun-Lei Tang (2016)

Annales Polonici Mathematici

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We study the following singular elliptic equation with critical exponent ⎧ - Δ u = Q ( x ) u 2 * - 1 + λ u - γ in Ω, ⎨u > 0 in Ω, ⎩u = 0 on ∂Ω, where Ω ⊂ ℝ N (N≥3) is a smooth bounded domain, and λ > 0, γ ∈ (0,1) are real parameters. Under appropriate assumptions on Q, by the constrained minimizer and perturbation methods, we obtain two positive solutions for all λ > 0 small enough.