Results 31 to 40 of about 4,182 (106)
Asymptotic boundary estimates for solutions to the p-Laplacian with infinite boundary values
Boundary Value Problems, 2019 In this paper, by using Karamata regular variation theory and the method of upper and lower solutions, we mainly study the second order expansion of solutions to the following p-Laplacian problems: Δpu=b(x)f(u),u>0,x∈Ω,u|∂Ω=∞ $\Delta _{p} u=b(x)f(u), u>0,
Ling Mi
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, 2021 . In this paper, by sub-supersolution methods, Karamata regular variation theory and perturbation method, we study the existence, uniqueness and asymptotic behavior of solutions near the boundary to quasilinear elliptic problem where Ω is a bounded ...
Chunlian Liu
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The existence and asymptotic behavior of boundary blow-up solutions to the k-Hessian equation
Journal of Differential Equations, 2019 In this paper we consider the existence and asymptotic behavior of k-convex solution to the boundary blow-up k-Hessian problem S k ( D 2 u ) = H ( x ) f ( u ) for x ∈ Ω , u ( x ) → + ∞ as dist ( x , ∂ Ω ) → 0 , where k ∈ { 1 , 2 , ⋯ , N } , S k ( D 2
Xuemei Zhang, M. Feng
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Elliptic operators on refined Sobolev scales on vector bundles
, 2017 We introduce a refined Sobolev scale on a vector bundle over a closed infinitely smooth manifold. This scale consists of inner product H\"ormander spaces parametrized with a real number and a function varying slowly at infinity in the sense of Karamata ...
Zinchenko, Tetiana
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Boundary blow-up solutions to the Monge-Ampère equation: Sharp conditions and asymptotic behavior
Advances in Nonlinear Analysis, 2019 Consider the boundary blow-up Monge-Ampère problem M[u]=K(x)f(u) for x∈Ω,u(x)→+∞ as dist(x,∂Ω)→0. $$\begin{array}{} \displaystyle M[u]=K(x)f(u) \mbox{ for } x \in {\it\Omega},\; u(x)\rightarrow +\infty \mbox{ as } {\rm dist}(x,\partial {\it\Omega ...
Xuemei Zhang, M. Feng
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Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in exterior domains
Electronic Journal of Differential Equations, 2018 In this article, we study the existence, uniqueness and the asymptotic behavior of a positive classical solution to the semilinear boundary value problem $$\displaylines{ -\Delta u=a(x)u^{\sigma }\quad \text{in }D, \cr u|_{\partial D}=0,\quad ...
Habib Maagli +2 more
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Beurling moving averages and approximate homomorphisms [PDF]
, 2014 The theory of regular variation, in its Karamata and Bojani\'c-Karamata/de Haan forms, is long established and makes essential use of homomorphisms. Both forms are subsumed within the recent theory of Beurling regular variation, developed further here ...
N. Bingham, A. Ostaszewski
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Asymptotic behavior of positive solutions of a semilinear Dirichlet problem outside the unit ball
Electronic Journal of Differential Equations, 2013 In this article, we are concerned with the existence, uniqueness and asymptotic behavior of a positive classical solution to the semilinear boundary-value problem $$displaylines{ -Delta u=a(x)u^{sigma }quadext{in }D, cr lim _{|x|o 1}u(x)= lim_{|x|o ...
Habib Maagli +2 more
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The Refined Sobolev Scale, Interpolation, and Elliptic Problems
, 2012 The paper gives a detailed survey of recent results on elliptic problems in Hilbert spaces of generalized smoothness. The latter are the isotropic H\"ormander spaces $H^{s,\varphi}:=B_{2,\mu}$, with $\mu(\xi)=^{s}\varphi()$ for $\xi\in\mathbb{R}^{n ...
Mikhailets, Vladimir A. +1 more
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Methods in half-linear asymptotic theory
Electronic Journal of Differential Equations, 2016 We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $$ (r(t)|y'|^{\alpha-1}\hbox{sgn} y')'=p(t)|y|^{\alpha-1}\hbox{sgn} y, $$ where r(t) and p(t) are positive continuous functions ...
Pavel Rehak
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