Results 21 to 30 of about 4,486,095 (208)

An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces

Advances in Nonlinear Analysis, 2020
It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.
Martínez Ángel D., Spector Daniel
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Existence and concentration behavior of solutions for a class of quasilinear elliptic equations with critical growth

Advances in Nonlinear Analysis, 2017
In this paper, we study a class of quasilinear elliptic equations involving the Sobolev critical ...
Teng Kaimin, Yang Xiaofeng
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Multiple boundary peak solutions for some singularly perturbed Neumann problems [PDF]

, 2000
We consider the problem \left \{ \begin{array}{rcl} \varepsilon^2 \Delta u - u + f(u) = 0 & \mbox{ in }& \ \Omega\\ u > 0 \ \mbox{ in} \ \Omega, \ \frac{\partial u}{\partial \nu} = 0 & \mbox{ on }& \ \partial\Omega, \end{array} \right. where \
Gui, Changfeng, Winter, M, Wei, Juncheng, Winter, Matthias, Juncheng Wei, Matthias Winter, Changfeng Gui, Gui, C, Wei, J   +8 more
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Semilinear elliptic partial differential equations with the critical Sobolev exponent [PDF]

, 2017
We present how variational methods and results from linear and non-linear functional analysis are applied to solving certain types of semilinear elliptic partial differential equations (PDEs).
Mavuso, Melusi Manqoba
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Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent

Boundary Value Problems, 2021
In this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.
Hongsen Fan, Zhiying Deng
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Schrödinger equation with critical Sobolev exponent

Differential and Integral Equations, 2004
In this paper we study the existence of solutions and their concentration phenomena of a singularly perturbed semilinear Schrodinger equation with the presence of the critical Sobolev exponent.
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A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝN

Advanced Nonlinear Studies, 2017
This paper concerns itself with the nonexistence and multiplicity of solutions for the following fractional Kirchhoff-type problem involving the critical Sobolev exponent:
Xiang Mingqi, Zhang Binlin, Zhang Xia
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Weighted Sobolev spaces on curves [PDF]

, 2002
45 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.MR#: MR1934626 (2003j:46038)Zbl#: Zbl 1019.46026In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non ...
Pestana, Domingo, Romera, Elena, Álvarez, Venancio, Rodríguez, José M.   +3 more
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A Nonlinear Elliptic PDE with Two Sobolev–Hardy Critical Exponents [PDF]

Archive for Rational Mechanics and Analysis, 2011
In this paper, we consider the following PDE involving two Sobolev-Hardy critical exponents, \label{0.1} {& Δu + λ\frac{u^{2^*(s_1)-1}}{|x|^{s_1}} + \frac{u^{2^*(s_2)-1}}{|x|^{s_2}} =0 \text{in} Ω, & u=0 \qquad \text{on} Ω, where $0 \le s_2 < s_1 \le 2$, $0 \ne λ\in \Bbb R$ and $0 \in \partial Ω$.
Li, YanYan, Lin, Chang-Shou
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The reaction–diffusion equation with Lewis function and critical Sobolev exponent [PDF]

, 2002
In this paper we consider the existence and asymptotic estimates of global solutions and finite time blowup of reaction–diffusion equation with Lewis function and critical Sobolev ...
Tan, Zhong
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