Results 31 to 40 of about 52,371 (280)
On a p-Laplacian system with critical Hardy–Sobolev exponents and critical Sobolev exponents [PDF]
We consider a quasilinear elliptic system involving the critical Hardy–Sobolev exponent and the Sobolev exponent. We use variational methods and analytic techniques to establish the existence of positive solutions of the system.
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On a Minimization Problem Involving the Critical Sobolev Exponent
Abstract Following [3] we study the following minimization problem: in any dimension n ≥ 4 and under suitable assumptions on a(x).
PRINARI F, VISCIGLIA, NICOLA
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The Kato Square Root Problem for Mixed Boundary Conditions [PDF]
We consider the negative Laplacian subject to mixed boundary conditions on a bounded domain. We prove under very general geometric assumptions that slightly above the critical exponent $\frac{1}{2}$ its fractional power domains still coincide with ...
Egert, Moritz+2 more
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An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces
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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A fractional Kirchhoff problem involving a singular term and a critical nonlinearity [PDF]
In this paper we consider the following critical nonlocal problem $$ \left\{\begin{array}{ll} M\left(\displaystyle\iint_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}}dxdy\right)(-\Delta)^s u = \displaystyle\frac{\lambda}{u^\gamma}+u^{2^*_s-1}&\quad ...
Fiscella, Alessio
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In this paper, we study a class of quasilinear elliptic equations involving the Sobolev critical ...
Teng Kaimin, Yang Xiaofeng
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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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Normalized solutions for nonlinear Kirchhoff type equations in high dimensions
We study the normalized solutions for nonlinear Kirchhoff equation with Sobolev critical exponent in high dimensions $ \mathbb{R}^N(N\geqslant4) $. In particular, in dimension $ N = 4 $, there is a special phenomenon for Kirchhoff equation that the mass ...
Lingzheng Kong, Haibo Chen
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Positive solutions for a class of singular quasilinear Schrödinger equations with critical Sobolev exponent [PDF]
We prove the existence of positive solutions of the following singular quasilinear Schrodinger equations at critical growth − Δ u − λ c ( x ) u − κ α ( Δ ( | u | 2 α ) ) | u | 2 α − 2 u = | u | q − 2 u + | u | 2 ⁎ − 2 u , u ∈ D 1 , 2 ( R N ) , via ...
Zhouxin Li
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Existence of solution to a critical equation with variable exponent [PDF]
In this paper we study the existence problem for the $p(x)-$Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not ...
Bonder, Julián Fernández+2 more
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