Geodesic
Eigenvalue problems for $p(x)$-Kirchhoff type equations
Electronic Journal of Differential Equations, Tome 2013 (2013).

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

Summary: In this article, we study the nonlocal $$\displaylines{ -M\Big(\int_{\Omega}\frac{1}{p(x)}|\nabla u|^{p(x)}dx\Big) \hbox{div}(|\nabla u|^{p(x)-2}\nabla u)= \lambda|u|^{q(x)-2}u \quad { in } \Omega,\cr u=0 \quad {on } \partial\Omega, }$$ By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish conditions for the existence of weak solutions.
Classification : 35J60, 35J35, 35J70
Keywords: $p(x)$-Kirchhoff type equations, variational methods, boundary value problems 
@article{EJDE_2013__2013__a56,
     author = {Afrouzi, Ghasem A. and Mirzapour, Maryam},
     title = {Eigenvalue problems for $p(x)${-Kirchhoff} type equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a56/}
}
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Afrouzi, Ghasem A.; Mirzapour, Maryam. Eigenvalue problems for $p(x)$-Kirchhoff type equations. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a56/