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Existence of Weak Solutions for Weighted Robin Problem Involving \(p\left( .\right)\)-biharmonic operator

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Abstract

Using Mountain Pass Theorem, we consider the existence of weak solutions of weighted Robin problem involving \(p\left( .\right)\)-biharmonic operator

$$\begin{aligned} \left\{ \begin{array}{cc} a\left( x\right) \Delta _{p\left( x\right) }^{2}u=\lambda b(x)\left| u\right| ^{q(x)-2}u, &{} in~\Omega \\ a(x)\left| \Delta u\right| ^{p(x)-2}\frac{\partial u}{\partial \upsilon }+\beta (x)\left| u\right| ^{p(x)-2}u=0, &{} on~\partial \Omega \end{array} \right. \end{aligned}$$

under some conditions in the space \(W_{a,b}^{2,p(.)}\left( \Omega \right) .\)

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Authors and Affiliations

  1. Department of Mathematics, Amasya University, Amasya, Turkey

    Öznur Kulak

  2. Department of Mathematics, Sinop University, Sinop, Turkey

    Ismail Aydin & Cihan Unal

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  1. Öznur Kulak
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  2. Ismail Aydin
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  3. Cihan Unal
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Correspondence to Cihan Unal.

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Kulak, Ö., Aydin, I. & Unal, C. Existence of Weak Solutions for Weighted Robin Problem Involving \(p\left( .\right)\)-biharmonic operator. Differ Equ Dyn Syst (2022). https://doi.org/10.1007/s12591-022-00619-6

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