Geodesic
Eigenvalue problems for \(p(x)\)-Kirchhoff type equations
Electronic journal of differential equations, Tome 2013 (2013)
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__a156,
     author = {Afrouzi,  Ghasem A. and Mirzapour,  Maryam},
     title = {Eigenvalue problems for {\(p(x)\)-Kirchhoff} type equations},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1359.35120},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a156/}
}
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AU  - Mirzapour,  Maryam
TI  - Eigenvalue problems for \(p(x)\)-Kirchhoff type equations
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a156/
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%A Mirzapour,  Maryam
%T Eigenvalue problems for \(p(x)\)-Kirchhoff type equations
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a156/
%G en
%F EJDE_2013__2013__a156
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__a156/