Solutions of stationary Kirchhoff equations involving nonlocal operators with critical nonlinearity in RN [PDF]
Nonlinear Analysis, 2017 In this paper, we consider the existence and multiplicity of solutions for fractional Schrödinger equations with critical nonlinearity in RN. We use the fractional version of Lions' second concentration-compactness principle and concentration-compactness
Ziwei Piao, Chenxing Zhou, Sihua Liang
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Homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign nonlinearities [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we
Dong-Lun Wu
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Lower Semicontinuity of Functionals via the Concentration-Compactness Principle
Journal of Mathematical Analysis and Applications, 2001 AbstractIn this paper we show the weak lower semicontinuity of some classes of functionals, using the concentration-compactness principle of P. L. Lions. These functionals involve an integral term, and we do not know whether it can be handled by the De Giorgi theorem.
Eugenio Montefusco
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Concentration-compactness principle for mountain pass problems
, 2005 In the paper we show that critical sequences associated with the mountain pass level for semilinear elliptic problems on $\R^N$ converge when the non-linearity is subcritical, superlinear and satisfies the penalty condition $F_\infty(s)
Kyril Tintarev
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Concentration-compactness principle for embedding into multiple exponential spaces on unbounded domains [PDF]
Czechoslovak Mathematical Journal, 2015 Let Ω ⊂ ℝ n be a domain and let α < n − 1. We prove the Concentration-Compactness Principle for the embedding of the space W 0 1 L n log α
Robert Černý
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The Concentration-Compactness Principle in the Calculus of Variations. The limit case, Part 1
Revista Matemática Iberoamericana, 1985 After the study made in the locally compact case for variational problems with some translation invariance, we investigate here the variational problems (with constraints) for example in \mathbb R^N where the invariance of \mathbb R^N
Pierre‐Louis Lions
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The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. [PDF]
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1984 In this paper (sequel of Part 1) we investigate further applications of the concentration-compactness principle to the solution of various minimization problems in unbounded domains. In particular we present here the solution of minimization problems associated with nonlinear field equations.
Pierre‐Louis Lions
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Note on the concentration-compactness principle for generalized Moser-Trudinger inequalities
Open Mathematics, 2012 Abstract Let Ω ⊂ ℝn, n ≥ 2, be a bounded domain and let α < n − 1. Motivated by Theorem I.6 and Remark I.18 of [Lions P.-L., The concentration-compactness principle in the calculus of variations. The limit case. I, Rev. Mat. Iberoamericana, 1985, 1(1), 145–201] and by the results of [Černý R., Cianchi A., Hencl S., Concentration ...
Černý Robert
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EXISTENCE OF STEADY STATES FOR THE MAXWELL–SCHRÖDINGER–POISSON SYSTEM: EXPLORING THE APPLICABILITY OF THE CONCENTRATION–COMPACTNESS PRINCIPLE [PDF]
Mathematical Models and Methods in Applied Sciences, 2013 This paper reviews recent results and open problems concerning the existence of steady states to the Maxwell–Schrödinger system. A combination of tools, proofs and results are presented in the framework of the concentration–compactness method.
Isabelle Catto +3 more
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Concentration-Compactness Principle for embedding into multiple exponential spaces [PDF]
Mathematical Inequalities & Applications, 2012 Let Ω⊂Rn , n 2 , be a bounded domain and let α < n−1 . We prove the ConcentrationCompactness Principle for the embedding of the Orlicz-Sobolev space W 1 0 L n logn−1 L logα logL(Ω) into the Orlicz space corresponding to a Young function that behaves like exp(exp(t n n−1−α )) for large t .
Robert Černɓ
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