Mountain pass solution for a p(x)-biharmonic Kirchhoff type equation

Document Type : Research Articles

Author

Department of Mathematics, Faculty of Mathematical Sciences, Farhangian University , Tehran, Iran

Abstract

In this paper we deal with the existence of weak solution for a

p (x)

-Kirchhoff type problem of the following form

{\begin{cases} - (a - b \int_{Ω} \frac{1}{p (x)} | Δ u |^{p (x)} d x) Δ (| Δ u |^{p (x) - 2} Δ u) = λ | u |^{p (x) - 2} u + g (x, u) & in Ω, \\ u = Δ u = 0 & on \partial Ω . \end{cases}

Using the Mountain Pass Theoem, we establish conditions ensuring the existence result.

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Main Subjects