Solutions of an anisotropic nonlocal problem involving variable exponent
[ X ]
Tarih
2013
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Walter De Gruyter Gmbh
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Anisotropic P(.)-Laplacian, Nonlocal Problem, Anisotropic Variable Exponent Lebesgue-Sobolev Spaces, Mountain Pass Theorem
Kaynak
Advances in Nonlinear Analysis
WoS Q Değeri
N/A
Scopus Q Değeri
Q1
Cilt
2
Sayı
3
