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Existence and multiplicity of weak solutions for eigenvalue Robin problem with weighted p(.)-Laplacian

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Abstract

By applying Mountain Pass Lemma, Ekeland’s variational principle and Fountain Theorem, we prove the existence and multiplicity of solutions for the following Robin problem

$$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} -\text {div}\left( a(x)\left| \nabla u\right| ^{p(x)-2}\nabla u\right) =\lambda b(x)\left| u\right| ^{q(x)-2}u, &{} x\in \varOmega \\ a(x)\left| \nabla u\right| ^{p(x)-2}\frac{\partial u}{\partial \upsilon }+\beta (x)\left| u\right| ^{p(x)-2}u=0, &{} x\in \partial \varOmega , \end{array}\right. \end{aligned}$$

under some appropriate conditions in the space \(W_{a,b}^{1,p(.)}\left( \varOmega \right) \).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Sinop University, Sinop, Turkey

    Ismail Aydin

  2. Republic of Turkey, Assessment, Selection and Placement Center, Ankara, Turkey

    Cihan Unal

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  1. Ismail Aydin
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  2. Cihan Unal
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Correspondence to Cihan Unal.

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Aydin, I., Unal, C. Existence and multiplicity of weak solutions for eigenvalue Robin problem with weighted p(.)-Laplacian. Ricerche mat 72, 511–528 (2023). https://doi.org/10.1007/s11587-021-00621-0

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  • DOI: https://doi.org/10.1007/s11587-021-00621-0

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