On a nonlocal elliptic problem

Andrzej Raczyński

Displaying similar documents to “On a nonlocal elliptic problem”

Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

Piotr Biler, Danielle Hilhorst, Tadeusz Nadzieja (1994)

Colloquium Mathematicae

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We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.

Oblique boundary value problems for nonlinear parabolic equations

Uraltseva, N. N.

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Harnack inequalities and ABP estimates for nonlinear second-order elliptic equations in unbounded domains.

Amendola, M.E., Rossi, L., Vitolo, A. (2008)

Abstract and Applied Analysis

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On the stability of solutions of nonlinear parabolic differential-functional equations

Stanisław Brzychczy (1996)

Annales Polonici Mathematici

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We consider a nonlinear differential-functional parabolic boundary initial value problem (1) ⎧A z + f(x,z(t,x),z(t,·)) - ∂z/∂t = 0 for t > 0, x ∈ G, ⎨z(t,x) = h(x) for t > 0, x ∈ ∂G, ⎩z(0,x) = φ₀(x) for x ∈ G, and the associated elliptic boundary value problem with Dirichlet condition (2) ⎧Az + f(x,z(x),z(·)) = 0 for x ∈ G, ⎨z(x) = h(x) for x ∈ ∂G ⎩ where $x = (x ₁, . . ., x_{m}) \in G \subset ℝ^{m}$ , G is an open and bounded domain with $C^{2 + α}$ (0 < α ≤ 1) boundary, the operator Az := ∑j,k=1m ajk(x) (∂²z/(∂xj...

Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients

Fabio Punzo, Alberto Tesei (2009)

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

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$L^{\infty}$ -estimates for nonlinear parabolic equations with natural growth conditions

Vincenzo Vespri (1993)

Rendiconti del Seminario Matematico della Università di Padova

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Large solutions of quasilinear elliptic system of competitive type: existence and asymptotic behavior.

Wei, Lin, Yang, Zuodong (2010)

International Journal of Differential Equations

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On positive solutions of quasilinear elliptic systems

Yuanji Cheng (1997)

Czechoslovak Mathematical Journal

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In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems $\}\begin{matrix} - Δ_{p} u = f (x, u, v), & in Ω, - Δ_{p} v = g (x, u, v), & in Ω, u = v = 0, & on \partial Ω, \end{matrix}$ where $- Δ_{p}$ is the $p$ -Laplace operator, $p > 1$ and $Ω$ is a $C^{1, α}$ -domain in $ℝ^{n}$ . We prove an analogue of [7, 16] for the eigenvalue problem with $f (x, u, v) = λ_{1} v^{p - 1}$ , $g (x, u, v) = λ_{2} u^{p - 1}$ and obtain a non-existence result of positive solutions for the general systems.

On a comparison principle for a quasilinear elliptic boundary value problem of a nonmonotone type

Michal Křížek, Liping Liu (1996)

Applicationes Mathematicae

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A nonlinear elliptic partial differential equation with the Newton boundary conditions is examined. We prove that for greater data we get a greater weak solution. This is the so-called comparison principle. It is applied to a steady-state heat conduction problem in anisotropic magnetic cores of large transformers.