Geodesic
Solutions of $p(x)$-Laplacian equations with critical exponent and perturbations in $R^N$
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Based on the theory of variable exponent Sobolev spaces, we study a class of $p(x)$-Laplacian equations in $\mathbb{R}^{N}$ involving the critical exponent. Firstly, we modify the principle of concentration compactness in $W^{1,p(x)}(\mathbb{R}^{N})$ and obtain a new type of Sobolev inequalities involving the atoms. Then, by using variational method, we obtain the existence of weak solutions when the perturbation is small enough.
Classification : 35J60, 46E35
Keywords: variable exponent Sobolev space, critical exponent, weak solution 
@article{EJDE_2012__2012__a90,
     author = {Zhang, Xia and Fu, Yongqiang},
     title = {Solutions of $p(x)${-Laplacian} equations with critical exponent and perturbations in $R^N$},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a90/}
}
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Zhang, Xia; Fu, Yongqiang. Solutions of $p(x)$-Laplacian equations with critical exponent and perturbations in $R^N$. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a90/