Results 11 to 20 of about 87,459 (144)
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 We present here a new method for solving minimization problems in unbounded domains. We first derive a general principle showing the equivalence between the compactness of all minimizing sequences and some strict sub-additivity conditions. The proof is based upon a compactness lemma obtained with the help of the notion of concentration function of a ...
P. Lions
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Concentration-compactness principle for Trudinger–Moser inequalities on Heisenberg groups and existence of ground state solutions [PDF]
Calculus of Variations and Partial Differential Equations, 2017 Let $$\mathbb {H}^{n}=\mathbb {C}^{n}\times \mathbb {R}$$Hn=Cn×R be the n-dimensional Heisenberg group, $$Q=2n+2$$Q=2n+2 be the homogeneous dimension of $$\mathbb {H}^{n}$$Hn. We extend the well-known concentration-compactness principle on finite domains
Jungang Li, G. Lu, Maochun Zhu
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The concentration-compactness principle in the Calculus of Variations
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 RN where the invariance of RN by the group of dilatations creates ...
P. Lions
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The concentration-compactness principles for $W^{s,p(\cdot,\cdot)}(\mathbb{R}^N)$ and application
, 2019 We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.
Ky Ho, Yun-Ho Kim
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Fractional Calculus and Applied AnalysisWe obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of ...
Nabil Chems Eddine +2 more
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Multiplicity results for generalized quasilinear critical Schrödinger equations in $${\mathbb {R}}^N$$ [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2023 Multiplicity results are proved for solutions both with positive and negative energy, as well as nonexistence results, of a generalized quasilinear Schrödinger potential free equation in the entire $${\mathbb {R}}^N$$ R N involving a ...
Laura Baldelli, Roberta Filippucci
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Critical Kirchhoff equations involving the -sub-Laplacians operators on the Heisenberg group
Bulletin of Mathematical Sciences, 2023 In this paper, we deal with a class of Kirchhoff-type critical elliptic equations involving the [Formula: see text]-sub-Laplacians operators on the Heisenberg group of the form M(∥DHu∥pp + ∥u∥ p,Vp)[−Δ H,pu + V (ξ)|u|p−2u] = λf(ξ,u) + |u|p∗−2u,ξ ∈ ℍn,u ...
Xueqi Sun +3 more
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AIMS Mathematics, 2023 We prove the existence and multiplicity of solutions for a class of Choquard-Kirchhoff type equations with variable exponents and critical reaction.
Lulu Tao, Rui He, Sihua Liang, Rui Niu
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A Remark on the Concentration Compactness Principle in Critical Dimension [PDF]
Communications on Pure and Applied Mathematics, 2021 AbstractWe prove some refinements of the concentration compactness principle for Sobolev space W1, n on a smooth compact Riemannian manifold of dimension n. As an application, we extend Aubin's theorem for functions on with zero first‐order moments of the area element to the higher‐order moments case.
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Ciência Rural, 2022 : Osmotic dehydration (OD) is a technique used for the partial removal of water from foodstuff, including fruit and vegetables, with the aim of producing a desiccated product. The process involves placing the material in a hypertonic solution for several
Barbara de Sousa Pinto +3 more
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