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    Solutions of an anisotropic nonlocal problem involving variable exponent
    (Walter De Gruyter Gmbh, 2013) Avci, Mustafa; Ayazoglu (Mashiyev), Rabil A.; Cekic, Bilal
    The present paper deals with an anisotropic Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Omega of R-N (N >= 3). The problem studied is a stationary version of the original Kirchhoff equation, involving the anisotropic (p) over right arrow( . )-Laplacian operator, in the framework of the variable exponent Lebesgue and Sobolev spaces. The question of the existence of weak solutions is treated. Applying the Mountain Pass Theorem of Ambrosetti and Rabinowitz, the existence of a nontrivial weak solution is obtained in the anisotropic variable exponent Sobolev space W-0(1,(p) over right arrow(.))(Omega), provided that the positive parameter lambda that multiplies the nonlinearity f is small enough.