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An improvement on the concentration-compactness principle
Acta Mathematicae Applicatae Sinica, 2001In this paper we first improve the concentration-compactness lemma by proving that the vanishing case is a special case of dichotomy, then we apply this improved concentration-compactness lemma to a typical restcted minimization problem, and get some new results.
Qiu Xing +3 more
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THE CONCENTRATION-COMPACTNESS PRINCIPLE AND INVERSE POWER METHOD
Acta Mathematica Scientia, 1990Abstract In this paper, we are concerned with the eigenvalue problem of a semilinear elliptic equation. We use concentration-compactness principle and inverse power method to find some conditions in order that the non-radial solutions may exist for an equation with variable coefficients.
Yi Ding, Xiaxi Ding
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Concentration-Compactness Principle for Generalized Trudinger Inequalities
Zeitschrift für Analysis und ihre Anwendungen, 2011Let \Omega\subset\mathbb R^n , n\geq 2 , be a bounded domain and let \alpha < n-1 . We prove the Concentration-Compactness Principle for the embedding of the Orlicz-Sobolev space
Stanislav Hencl +2 more
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THE CONCENTRATION-COMPACTNESS PRINCIPLE IN NONLINEAR ELLIPTIC EQUATIONS
Acta Mathematica Scientia, 1989Abstract In this paper we discuss various kinds of eigenvalue problems by an improved Concentration-compactness principle. We also obtain a global compactness lemma and apply it to discuss the role of the symmetry in compactness.
Daomin Cao, Xiping Zhu
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Concentration-compactness principle for an inequality by D. Adams
Calculus of Variations and Partial Differential Equations, 2013This paper brings a generalization of the Lions concentration–compactness principle to the Sobolev space \(W_0^{m,p}(\Omega )\) when \(mp=n\) and \(\Omega \subset \mathbb {R}^n \, (n \ge 2)\) is a smooth domain with finite \(n\)-measure. Moreover, our result sharpens an inequality by D. Adams improving its best exponent.
Abiel Costa Macedo, João Marcos do Ó
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Concentration-compactness principle and extremal functions for a sharp Trudinger-Moser inequality
Calculus of Variations and Partial Differential Equations, 2014We prove a concentration-compactness principle for the Trudinger-Moser functional associated with a class of weighted Sobolev spaces including fractional dimensions. Based in this result and using blow up analysis we establish a sharp form of Trudinger-Moser type inequality for this class of weighted Sobolev spaces.
José Francisco de Oliveira +2 more
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The principle of concentration compactness in spaces and its application
Nonlinear Analysis: Theory, Methods & Applications, 2009Abstract In this paper we establish a principle of concentration compactness in L p ( x ) spaces and apply it to obtain the existence of solutions for p ( x ) -Laplacian equations with critical growth.
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An abstract version of the concentration compactness principle
2002International ...
Schindler, Ian, Tintarev, Cyril
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Nonlinear Analysis, 2020
Abstract In this paper, we establish a sharp concentration-compactness principle associated with the Trudinger–Moser inequality on Sobolev spaces with logarithmic weights. As applications, we establish the existence of ground state solutions to the following equation with critical double exponential nonlinearity − d i v ( | ∇ u |
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Abstract In this paper, we establish a sharp concentration-compactness principle associated with the Trudinger–Moser inequality on Sobolev spaces with logarithmic weights. As applications, we establish the existence of ground state solutions to the following equation with critical double exponential nonlinearity − d i v ( | ∇ u |
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