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Universal Journal of Applied Mathematics Vol. 2(3), pp. 153 - 159
DOI: 10.13189/ujam.2014.020306
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Existence Results for a Nonlocal Problem Involving the p-Laplace Operator

Mustafa Avci ^*
Faculty of Economics and Administrative Sciences, Batman University, 72000-Batman, Turkey

ABSTRACT

The present paper deals with a nonlocal problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain 惟 of R^N. The problem studied is a stationary version of the original Kirchhoff equation involving the p-Laplace operator. The question of the existence of weak solutions is treated. Using variational approach and applying the Mountain Pass Theorem together with Fountain theorem, the existence and multiplicity of solutions is obtained in the Sobolev space W^1,p(惟).

KEYWORDS
Variational Method, Nonlocal Problem, Mountain-pass Theorem, Fountain Theorem

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mustafa Avci , "Existence Results for a Nonlocal Problem Involving the p-Laplace Operator," Universal Journal of Applied Mathematics, Vol. 2, No. 3, pp. 153 - 159, 2014. DOI: 10.13189/ujam.2014.020306.

(b). APA Format:
Mustafa Avci (2014). Existence Results for a Nonlocal Problem Involving the p-Laplace Operator. Universal Journal of Applied Mathematics, 2(3), 153 - 159. DOI: 10.13189/ujam.2014.020306.