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Title
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EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR NONLOCAL −→p (x)-LAPLACIAN PROBLEM
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Type
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JournalPaper
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Keywords
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Anisotropic Sobolev spaces, Variable exponent, Mountain pass theorem, Fountain theorem, Dual Fountain theorem
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Abstract
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In this paper, we study the nonlocal anisotropic −→p (x)-Laplacian problem of the following form − N i=1 Mi Ω |∂xiu|pi(x) pi(x) dx ∂xi |∂xiu|pi(x)−2∂xiu = f(x, u) in Ω, u = 0 on ∂Ω. By means of a direct variational approach and the theory of the anisotropic variable exponent Sobolev space, we obtain the existence and multiplicity of weak energy solutions. Moreover, we get much better results with f in a special form.
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Researchers
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maryam mirzapour (Second Researcher), Ghasem Alizadeh Afrouzi (First Researcher)
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