Results 11 to 20 of about 33,794 (182)
The concentration-compactness principle for variable exponent spaces and applications [PDF]
Electronic Journal of Differential Equations, 2009 In this article, we extend the well-known concentration - compactness principle by Lions to the variable exponent case. We also give some applications to the existence problem for the p(x)-Laplacian with critical growth.
Fernandez Bonder, Julian, Silva, Analia
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Existence of solution to a critical equation with variable exponent [PDF]
, 2012 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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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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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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Existence of Solutions for p-Kirchhoff Problem of Brézis-Nirenberg Type with Singular Terms
Journal of Function Spaces, 2022 In this paper, we prove the existence of positive solution for a p-Kirchhoff problem of Brézis-Nirenberg type with singular terms, nonlocal term, and the Caffarelli-Kohn-Nirenberg exponent by using variational methods, concentration compactness, and ...
Atika Matallah +2 more
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Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities [PDF]
, 2017 A nonlinear Schr\"odinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integro-differential type and it arises naturally in modeling fiber-optics communication systems with periodically ...
Hundertmark, Dirk +3 more
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Nodal solutions for the Choquard equation [PDF]
, 2016 We consider the general Choquard equations $$ -\Delta u + u = (I_\alpha \ast |u|^p) |u|^{p - 2} u $$ where $I_\alpha$ is a Riesz potential. We construct minimal action odd solutions for $p \in (\frac{N + \alpha}{N}, \frac{N + \alpha}{N - 2})$ and ...
Ghimenti, Marco, Van Schaftingen, Jean
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Concentration analysis and cocompactness [PDF]
, 2013 Loss of compactness that occurs in may significant PDE settings can be expressed in a well-structured form of profile decomposition for sequences. Profile decompositions are formulated in relation to a triplet $(X,Y,D)$, where $X$ and $Y$ are Banach ...
C Clark +39 more
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Ground states for scalar field equations with anisotropic nonlocal nonlinearities [PDF]
, 2014 We consider a class of scalar field equations with anisotropic nonlocal nonlinearities. We obtain a suitable extension of the well-known compactness lemma of Benci and Cerami to this variable exponent setting, and use it to prove that the Palais-Smale ...
Iannizzotto, Antonio +2 more
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Semiclassical stationary states for nonlinear Schr\"odinger equations under a strong external magnetic field [PDF]
, 2015 We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega, \end{aligned}
Di Cosmo, Jonathan +1 more
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