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The concentration-compactness principle for Musielak-Orlicz spaces and applications [PDF]
This paper extends the Concentration-Compactness Principle to Musielak-Orlicz spaces, working in both bounded and unbounded domains. We show that our results include important special cases like classical Orlicz spaces, variable exponent spaces, double phase spaces, and a new type of double phase problem where the exponents depend on the solution ...
Ala Eddine Bahrouni, Anouar Bahrouni
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A concentration-compactness principle for perturbed isoperimetric problems with general assumptions [PDF]
Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely'' distant from each other. In this article and under mild assumptions we establish existence and density estimates of generalized minimizers of perturbed ...
Jules Candau-Tilh
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The concentration-compactness principle for fractional Orlicz-Sobolev spaces
Complex Variables and Elliptic EquationsIn this paper, we delve into the well-known concentration-compactness principle in fractional Orlicz-Sobolev spaces, and we apply it to establish the existence of a weak solution for a critical elliptic problem involving the fractional $g-$Laplacian.
Sabri Bahrouni, Olı́mpio H. Miyagaki
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Fractional Calculus and Applied AnalysisAbstractWe 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 nonlinear critical anisotropic elliptic equations involving variable exponents and two real ...
Nabil Chems Eddine +2 more
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Concentration-compactness results for systems in the Heisenberg group [PDF]
Opuscula Mathematica, 2020 In this paper we complete the study started in [P. Pucci, L. Temperini, Existence for (p,q) critical systems in the Heisenberg group, Adv. Nonlinear Anal.
Patrizia Pucci, Letizia Temperini
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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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The Existence Result for a p-Kirchhoff-Type Problem Involving Critical Sobolev Exponent
Journal of Function Spaces, 2023 In this paper, by using the mountain pass theorem and the concentration compactness principle, we prove the existence of a positive solution for a p-Kirchhoff-type problem with critical Sobolev exponent.
Hayat Benchira +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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Young measures in a nonlocal phase transition problem [PDF]
, 1997 A nonlocal variational problem modelling phase transitions is studied in the framework of Young measures. The existence of global minimisers among functions with internal layers on an infinite tube is proved by combining a weak convergence result ...
Ren, X, Winter, M
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